A Jacquet-Langlands functor for $p$-adic locally analytic representations

Gabriel Dospinescu; Juan Esteban Rodr\'iguez Camargo

arxiv: 2411.17082 · v3 · submitted 2024-11-26 · 🧮 math.NT · math.RT

A Jacquet-Langlands functor for p-adic locally analytic representations

Gabriel Dospinescu , Juan Esteban Rodr\'iguez Camargo This is my paper

Pith reviewed 2026-05-23 16:56 UTC · model grok-4.3

classification 🧮 math.NT math.RT

keywords local Shimura varietiesp-adic Jacquet-Langlands functorlocally analytic representationsperiod sheavesinfinite levelde Rham cohomologyp-adic Lie groupsJacquet-Langlands correspondence

0 comments

The pith

Locally analytic vectors of period sheaves on dual local Shimura varieties are independent of the p-adic Lie group actions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that when two local Shimura varieties are dual, the locally analytic vectors of their period sheaves at infinite level do not depend on the actions of the corresponding p-adic Lie groups G and Gb. This generalizes an earlier result of Pan that covered only the Lubin-Tate and Drinfeld spaces for GL2. The independence is then used to prove that Scholze's p-adic Jacquet-Langlands functor commutes with passage to locally analytic vectors and respects central characters of the Lie algebras. The paper also shows that the compactly supported de Rham cohomology of the two towers is isomorphic as a smooth representation of the product group G times Gb.

Core claim

In the setting of dual local Shimura varieties with compatible period sheaves at infinite level, the locally analytic vectors of these sheaves are independent of the actions of the p-adic Lie groups G and Gb. This independence implies that Scholze's p-adic Jacquet-Langlands functor commutes with the passage to locally analytic vectors and is compatible with central characters of Lie algebras. The compactly supported de Rham cohomology of the two towers is moreover isomorphic as a smooth representation of G times Gb.

What carries the argument

The independence of locally analytic vectors from the actions of G and Gb on period sheaves at infinite level, under the assumption of duality between local Shimura varieties.

If this is right

Scholze's p-adic Jacquet-Langlands functor commutes with passage to locally analytic vectors.
The functor is compatible with central characters of the Lie algebras.
The compactly supported de Rham cohomologies of the two towers are isomorphic as smooth representations of G times Gb.
The independence generalizes Pan's result from the GL2 Lubin-Tate and Drinfeld cases to arbitrary dual pairs where the setup holds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The independence result could be tested directly on known dual pairs in low rank to verify the claimed lack of dependence.
The isomorphism of de Rham cohomologies may extend to other cohomology theories if the period sheaves admit similar comparisons.
The commutation property might allow the functor to be applied in settings where only locally analytic data is computable.

Load-bearing premise

The existence of a duality between the two local Shimura varieties together with compatible period sheaves at infinite level whose locally analytic vectors can be compared after base change or restriction.

What would settle it

An explicit pair of dual local Shimura varieties in which the locally analytic vectors of the period sheaves depend on the action of G or Gb, or in which the p-adic Jacquet-Langlands functor fails to commute with taking locally analytic vectors.

read the original abstract

We study the locally analytic theory of infinite level local Shimura varieties. As a main result, we prove that in the case of a duality of local Shimura varieties, the locally analytic vectors of different period sheaves at infinite level are independent of the actions of the $p$-adic Lie groups $G$ and $G_b$ of the two towers; this generalizes a result of Pan for the Lubin-Tate and Drinfeld spaces for $\mathrm{GL}_2$. We apply this theory to show that Scholze's $p$-adic Jacquet-Langlands functor commutes with the passage to locally analytic vectors, and is compatible with central characters of Lie algebras. We also prove that the compactly supported de Rham cohomology of the two towers are isomorphic as smooth representations of $G\times G_b$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proves conditional independence of locally analytic vectors under duality of local Shimura varieties and applies it to commutation with the p-adic Jacquet-Langlands functor.

read the letter

The punchline is that this paper proves an independence result for locally analytic vectors of period sheaves in dual local Shimura varieties, showing they don't depend on the G and G_b actions. This generalizes Pan's earlier work on the GL_2 case and is used to prove that Scholze's p-adic Jacquet-Langlands functor commutes with taking locally analytic vectors while respecting Lie algebra central characters. They also establish an isomorphism of the compactly supported de Rham cohomologies as smooth representations of the product group.

Referee Report

1 major / 1 minor

Summary. The paper develops the locally analytic theory of infinite-level local Shimura varieties. Its main result states that, in the presence of a duality between two local Shimura varieties, the locally analytic vectors of the associated period sheaves at infinite level are independent of the actions of the p-adic Lie groups G and G_b; this generalizes Pan's earlier result for the Lubin-Tate and Drinfeld towers in the GL_2 case. The theory is then applied to prove that Scholze's p-adic Jacquet-Langlands functor commutes with passage to locally analytic vectors and respects central characters of the Lie algebras. A further unconditional result asserts that the compactly supported de Rham cohomology groups of the two towers are isomorphic as smooth representations of G × G_b.

Significance. If the stated results hold, the work supplies a useful generalization of known independence statements from the GL_2 setting to higher-rank groups, thereby furnishing technical tools for the study of p-adic automorphic forms and the p-adic Jacquet-Langlands correspondence in the locally analytic category. The cohomology isomorphism provides an additional concrete comparison between the two towers that may be of independent interest.

major comments (1)

The independence of locally analytic vectors (and therefore the claimed commutation of the Jacquet-Langlands functor with passage to locally analytic vectors) is explicitly conditional on the existence of a duality of local Shimura varieties together with compatible period sheaves at infinite level. The manuscript invokes this setup as given rather than constructing or verifying the required duality and compatibility inside the paper; consequently the main theorems remain conditional on external input whose availability beyond the GL_2 case is not addressed.

minor comments (1)

The abstract would benefit from a one-sentence indication of the main technical ingredients (e.g., properties of period sheaves or base-change arguments) used to establish independence, even if full details appear later.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its significance. We address the single major comment below.

read point-by-point responses

Referee: The independence of locally analytic vectors (and therefore the claimed commutation of the Jacquet-Langlands functor with passage to locally analytic vectors) is explicitly conditional on the existence of a duality of local Shimura varieties together with compatible period sheaves at infinite level. The manuscript invokes this setup as given rather than constructing or verifying the required duality and compatibility inside the paper; consequently the main theorems remain conditional on external input whose availability beyond the GL_2 case is not addressed.

Authors: We agree that the main results are stated under the hypothesis that a duality of local Shimura varieties exists together with compatible period sheaves at infinite level. The paper takes this setup as given (as is standard when generalizing results from the GL_2 case) and focuses on the consequences for locally analytic vectors, the p-adic Jacquet-Langlands functor, and de Rham cohomology. The existence of such dualities is known for the Lubin-Tate/Drinfeld towers by the work of Pan and is expected more generally from the theory of local Shimura varieties, but we will add an explicit remark in the introduction clarifying the conditional nature of the theorems and referencing the relevant literature on dualities. This revision will not change the statements of the theorems themselves. revision: partial

Circularity Check

0 steps flagged

No circularity: main result conditional on explicitly stated external duality assumption

full rationale

The paper explicitly frames its central theorem as holding under the given assumption of a duality of local Shimura varieties together with compatible period sheaves at infinite level. This setup is invoked as input rather than derived or fitted inside the manuscript, and the independence of locally analytic vectors from the G and G_b actions is stated as a consequence of that input (generalizing Pan). No equations reduce the claimed independence or functor commutation to a self-citation chain, a fitted parameter renamed as prediction, or a definitional equivalence. The derivation is therefore self-contained against the stated assumptions and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard setup of local Shimura varieties and period sheaves at infinite level; no free parameters are introduced in the abstract, no new entities are postulated, and the axioms are background facts from p-adic geometry.

axioms (2)

domain assumption Existence of dual local Shimura varieties equipped with compatible period sheaves at infinite level whose locally analytic vectors are well-defined.
Invoked to state the main independence result for the two towers.
domain assumption Scholze's p-adic Jacquet-Langlands functor is already defined on the relevant categories of representations.
Used when claiming commutation with passage to locally analytic vectors.

pith-pipeline@v0.9.0 · 5674 in / 1644 out tokens · 32455 ms · 2026-05-23T16:56:31.468603+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 1.3: G-locally analytic vectors of RΓv(eX, BI) are H-locally analytic; natural map RΓv(eX, BI)RG×H−la ≃ RΓv(eX, BI)RG−la
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Corollary 1.2 and Theorem 1.6: O^G-la_M = O^Gb-la_M; actions of n0_μ, n0_μ−1 vanish on O^la_M; central characters of m0_μ, m0_μ−1 agree

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

On Drinfeld's representability theorem
math.NT 2026-05 unverdicted novelty 5.0

New transparent proof of Drinfeld's representability theorem for moduli of p-divisible groups with extra actions, plus detailed presentation of the moduli space and formal model of the p-adic symmetric space.

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages · cited by 1 Pith paper · 2 internal anchors

[1]

Descent for solid quasi-coherent sheaves on perfectoid spaces

Johannes Ansch\"utz and Lucas Mann. Descent for solid quasi-coherent sheaves on perfectoid spaces. https://arxiv.org/abs/2403.01951, 2024

work page arXiv 2024
[2]

A 6 -functor formalism for solid quasi-coherent sheaves on the F argues- F ontaine curve

Johannes Ansch\"utz, Lucas Mann, and Arthur-C\'esar Le Bras. A 6 -functor formalism for solid quasi-coherent sheaves on the F argues- F ontaine curve. In preparation

work page
[3]

Localisation de g -modules

Alexandre Be linson and Joseph Bernstein. Localisation de g -modules. C. R. Acad. Sci. Paris S\' e r. I Math. , 292(1):15--18, 1981

work page 1981
[4]

Integral p -adic H odge theory

Bhargav Bhatt, Matthew Morrow, and Peter Scholze. Integral p -adic H odge theory. Publ. Math. Inst. Hautes \' E tudes Sci. , 128:219--397, 2018

work page 2018
[5]

The emerging p -adic L anglands programme

Christophe Breuil. The emerging p -adic L anglands programme. In Proceedings of the I nternational C ongress of M athematicians. V olume II , pages 203--230. Hindustan Book Agency, New Delhi, 2010

work page 2010
[6]

Cohomologie p -adique de la tour de D rinfeld: le cas de la dimension 1

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Cohomologie p -adique de la tour de D rinfeld: le cas de la dimension 1. J. Amer. Math. Soc. , 33(2):311--362, 2020

work page 2020
[7]

Integral p -adic \'etale cohomology of D rinfeld symmetric spaces

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Integral p -adic \'etale cohomology of D rinfeld symmetric spaces. Duke Math. J. , 170(3):575--613, 2021

work page 2021
[8]

Factorisation de la cohomologie \'etale p -adique de la tour de D rinfeld

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Factorisation de la cohomologie \'etale p -adique de la tour de D rinfeld. Forum Math. Pi , 11:Paper No. e16, 62, 2023

work page 2023
[9]

The $p$ -adic local langlands correspondence for $GL_2( Q _p)$

Pierre Colmez, Gabriel Dospinescu, and Vytautas Pa s k \=u nas. The $p$ -adic local langlands correspondence for $GL_2( Q _p)$ . Camb. J. Math. , 2(1):1--47, 2014

work page 2014
[10]

On the generic part of the cohomology of compact unitary S himura varieties

Ana Caraiani and Peter Scholze. On the generic part of the cohomology of compact unitary S himura varieties. Ann. of Math. (2) , 186(3):649--766, 2017

work page 2017
[11]

Lectures on C ondensed M athematics

Dustin Clausen and Peter Scholze. Lectures on C ondensed M athematics. https://www.math.uni-bonn.de/people/scholze/Condensed.pdf, 2019

work page 2019
[12]

Lectures on A nalytic G eometry

Dustin Clausen and Peter Scholze. Lectures on A nalytic G eometry. https://www.math.uni-bonn.de/people/scholze/Analytic.pdf, 2020

work page 2020
[13]

Rev\^etements du demi-plan de D rinfeld et correspondance de L anglands p -adique

Gabriel Dospinescu and Arthur-C\'esar Le Bras. Rev\^etements du demi-plan de D rinfeld et correspondance de L anglands p -adique. Ann. of Math. (2) , 186(2):321--411, 2017

work page 2017
[14]

On the interpolation of systems of eigenvalues attached to automorphic H ecke eigenforms

Matthew Emerton. On the interpolation of systems of eigenvalues attached to automorphic H ecke eigenforms. Invent. Math. , 164(1):1--84, 2006

work page 2006
[15]

A relation between two moduli spaces studied by V

Gerd Faltings. A relation between two moduli spaces studied by V . G . D rinfeld. In Algebraic number theory and algebraic geometry , volume 300 of Contemp. Math. , pages 115--129. Amer. Math. Soc., Providence, RI, 2002

work page 2002
[16]

L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld et applications cohomologiques

Laurent Fargues. L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld et applications cohomologiques. In L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld , volume 262 of Progr. Math. , pages 1--325. Birkh\"auser, Basel, 2008

work page 2008
[17]

Geometrization of the local L anglands correspondence, 2024

Laurent Fargues and Peter Scholze. Geometrization of the local L anglands correspondence, 2024

work page 2024
[18]

Rigid analytic spaces with overconvergent structure sheaf

Elmar Grosse-Kl \"o nne. Rigid analytic spaces with overconvergent structure sheaf. J. Reine Angew. Math. , 519:73--95, 2000

work page 2000
[19]

6- F unctor F ormalisms and S mooth R epresentations, 2024

Claudius Heyer and Lucas Mann. 6- F unctor F ormalisms and S mooth R epresentations, 2024

work page 2024
[20]

A generalization of formal schemes and rigid analytic varieties

Roland Huber. A generalization of formal schemes and rigid analytic varieties. Math. Z. , 217(4):513--551, 1994

work page 1994
[21]

\' E tale cohomology of rigid analytic varieties and adic spaces

Roland Huber. \' E tale cohomology of rigid analytic varieties and adic spaces . Aspects of Mathematics, E30. Friedr. Vieweg & Sohn, Braunschweig, 1996

work page 1996
[22]

Kedlaya, David Hansen, Bastian Haase, Shizhang Li, Ruochuan Liu, Peter Scholze, Annie Carter, Zonglin Jiang, Jake Postema, Daniel Aaron Smith, Claus Mazanti Sorensen, and Xin Tong

Kiran S. Kedlaya, David Hansen, Bastian Haase, Shizhang Li, Ruochuan Liu, Peter Scholze, Annie Carter, Zonglin Jiang, Jake Postema, Daniel Aaron Smith, Claus Mazanti Sorensen, and Xin Tong. Sheaves, stacks, and shtukas. Perfectoid Spaces , 2019

work page 2019
[23]

Kottwitz

Robert E. Kottwitz. Isocrystals with additional structure. II . Compos. Math. , 109(3):255--339, 1997

work page 1997
[24]

Higher topos theory , volume 170 of Ann

Jacob Lurie. Higher topos theory , volume 170 of Ann. Math. Stud. Princeton, NJ: Princeton University Press, 2009

work page 2009
[25]

Higher algebra

Jacob Lurie. Higher algebra. 2017

work page 2017
[26]

The 6-functor formalism for z_ - and q_ -sheaves on diamonds

Lucas Mann. The 6-functor formalism for Z _ - and Q _ -sheaves on diamonds. https://arxiv.org/abs/2209.08135, 2022

work page arXiv 2022
[27]

A p - A dic 6- F unctor F ormalism in R igid- A nalytic G eometry

Lucas Mann. A p -adic 6- F unctor F ormalism in R igid- A nalytic G eometry. https://arxiv.org/abs/2206.02022, 2022

work page arXiv 2022
[28]

On locally analytic vectors of the completed cohomology of modular curves

Lue Pan. On locally analytic vectors of the completed cohomology of modular curves. Forum of Mathematics, Pi , 10:e7, 2022

work page 2022
[29]

On locally analytic vectors of the completed cohomology of modular curves II

Lue Pan. On locally analytic vectors of the completed cohomology of modular curves II . https://arxiv.org/abs/2209.06366, 2022

work page arXiv 2022
[30]

Geometric S en theory over rigid analytic spaces, 2023

Juan Esteban Rodr\'iguez Camargo. Geometric S en theory over rigid analytic spaces, 2023

work page 2023
[31]

The analytic de rham stack in rigid geometry

Juan Esteban Rodr\'iguez Camargo. The analytic de rham stack in rigid geometry. https://arxiv.org/abs/2401.07738, 2024

work page arXiv 2024
[32]

Locally analytic completed cohomology, 2024

Juan Esteban Rodr\'iguez Camargo. Locally analytic completed cohomology, 2024

work page 2024
[33]

Solid locally analytic representations of $p$ -adic Lie groups

Joaqu \' n Rodrigues Jacinto and Juan Esteban Rodr \' guez Camargo. Solid locally analytic representations of $p$ -adic Lie groups. Represent. Theory , 26:962--1024, 2022

work page 2022
[34]

Solid locally analytic representations

Joaqu\'in Rodrigues Jacinto and Juan Esteban Rodr\'iguez Camargo. Solid locally analytic representations. https://arxiv.org/abs/2305.03162, 2023

work page internal anchor Pith review Pith/arXiv arXiv 2023
[35]

Towards a theory of local S himura varieties

Michael Rapoport and Eva Viehmann. Towards a theory of local S himura varieties. M\"unster J. Math. , 7(1):273--326, 2014

work page 2014
[36]

Rapoport and Th

M. Rapoport and Th. Zink. Period spaces for p -divisible groups , volume 141 of Annals of Mathematics Studies . Princeton University Press, Princeton, NJ, 1996

work page 1996
[37]

p -adic H odge theory for rigid-analytic varieties

Peter Scholze. p -adic H odge theory for rigid-analytic varieties. Forum Math. Pi , 1:e1, 77, 2013

work page 2013
[38]

On the p -adic cohomology of the L ubin- T ate tower

Peter Scholze. On the p -adic cohomology of the L ubin- T ate tower. Ann. Sci. \' E c. Norm. Sup\' e r. (4) , 51(4):811--863, 2018. With an appendix by Michael Rapoport

work page 2018
[39]

Etale cohomology of diamonds

Peter Scholze. Etale cohomology of diamonds. https://arxiv.org/abs/1709.07343v3, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[40]

Algebras of p -adic distributions and admissible representations

Peter Schneider and Jeremy Teitelbaum. Algebras of p -adic distributions and admissible representations. Invent. Math. , 153(1):145--196, 2003

work page 2003
[41]

Moduli of p -divisible groups

Peter Scholze and Jared Weinstein. Moduli of p -divisible groups. Camb. J. Math. , 1(2):145--237, 2013

work page 2013
[42]

Berkeley Lectures on p-adic Geometry: (AMS-207)

Peter Scholze and Jared Weinstein. Berkeley Lectures on p-adic Geometry: (AMS-207) . Princeton University Press, 2020

work page 2020
[43]

A motivic version of the theorem of F ontaine and W intenberger

Alberto Vezzani. A motivic version of the theorem of F ontaine and W intenberger. Compos. Math. , 155(1):38--88, 2019

work page 2019

[1] [1]

Descent for solid quasi-coherent sheaves on perfectoid spaces

Johannes Ansch\"utz and Lucas Mann. Descent for solid quasi-coherent sheaves on perfectoid spaces. https://arxiv.org/abs/2403.01951, 2024

work page arXiv 2024

[2] [2]

A 6 -functor formalism for solid quasi-coherent sheaves on the F argues- F ontaine curve

Johannes Ansch\"utz, Lucas Mann, and Arthur-C\'esar Le Bras. A 6 -functor formalism for solid quasi-coherent sheaves on the F argues- F ontaine curve. In preparation

work page

[3] [3]

Localisation de g -modules

Alexandre Be linson and Joseph Bernstein. Localisation de g -modules. C. R. Acad. Sci. Paris S\' e r. I Math. , 292(1):15--18, 1981

work page 1981

[4] [4]

Integral p -adic H odge theory

Bhargav Bhatt, Matthew Morrow, and Peter Scholze. Integral p -adic H odge theory. Publ. Math. Inst. Hautes \' E tudes Sci. , 128:219--397, 2018

work page 2018

[5] [5]

The emerging p -adic L anglands programme

Christophe Breuil. The emerging p -adic L anglands programme. In Proceedings of the I nternational C ongress of M athematicians. V olume II , pages 203--230. Hindustan Book Agency, New Delhi, 2010

work page 2010

[6] [6]

Cohomologie p -adique de la tour de D rinfeld: le cas de la dimension 1

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Cohomologie p -adique de la tour de D rinfeld: le cas de la dimension 1. J. Amer. Math. Soc. , 33(2):311--362, 2020

work page 2020

[7] [7]

Integral p -adic \'etale cohomology of D rinfeld symmetric spaces

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Integral p -adic \'etale cohomology of D rinfeld symmetric spaces. Duke Math. J. , 170(3):575--613, 2021

work page 2021

[8] [8]

Factorisation de la cohomologie \'etale p -adique de la tour de D rinfeld

Pierre Colmez, Gabriel Dospinescu, and Wies awa Nizio . Factorisation de la cohomologie \'etale p -adique de la tour de D rinfeld. Forum Math. Pi , 11:Paper No. e16, 62, 2023

work page 2023

[9] [9]

The \(p\) -adic local langlands correspondence for \(GL_2( Q _p)\)

Pierre Colmez, Gabriel Dospinescu, and Vytautas Pa s k \=u nas. The \(p\) -adic local langlands correspondence for \(GL_2( Q _p)\) . Camb. J. Math. , 2(1):1--47, 2014

work page 2014

[10] [10]

On the generic part of the cohomology of compact unitary S himura varieties

Ana Caraiani and Peter Scholze. On the generic part of the cohomology of compact unitary S himura varieties. Ann. of Math. (2) , 186(3):649--766, 2017

work page 2017

[11] [11]

Lectures on C ondensed M athematics

Dustin Clausen and Peter Scholze. Lectures on C ondensed M athematics. https://www.math.uni-bonn.de/people/scholze/Condensed.pdf, 2019

work page 2019

[12] [12]

Lectures on A nalytic G eometry

Dustin Clausen and Peter Scholze. Lectures on A nalytic G eometry. https://www.math.uni-bonn.de/people/scholze/Analytic.pdf, 2020

work page 2020

[13] [13]

Rev\^etements du demi-plan de D rinfeld et correspondance de L anglands p -adique

Gabriel Dospinescu and Arthur-C\'esar Le Bras. Rev\^etements du demi-plan de D rinfeld et correspondance de L anglands p -adique. Ann. of Math. (2) , 186(2):321--411, 2017

work page 2017

[14] [14]

On the interpolation of systems of eigenvalues attached to automorphic H ecke eigenforms

Matthew Emerton. On the interpolation of systems of eigenvalues attached to automorphic H ecke eigenforms. Invent. Math. , 164(1):1--84, 2006

work page 2006

[15] [15]

A relation between two moduli spaces studied by V

Gerd Faltings. A relation between two moduli spaces studied by V . G . D rinfeld. In Algebraic number theory and algebraic geometry , volume 300 of Contemp. Math. , pages 115--129. Amer. Math. Soc., Providence, RI, 2002

work page 2002

[16] [16]

L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld et applications cohomologiques

Laurent Fargues. L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld et applications cohomologiques. In L'isomorphisme entre les tours de L ubin- T ate et de D rinfeld , volume 262 of Progr. Math. , pages 1--325. Birkh\"auser, Basel, 2008

work page 2008

[17] [17]

Geometrization of the local L anglands correspondence, 2024

Laurent Fargues and Peter Scholze. Geometrization of the local L anglands correspondence, 2024

work page 2024

[18] [18]

Rigid analytic spaces with overconvergent structure sheaf

Elmar Grosse-Kl \"o nne. Rigid analytic spaces with overconvergent structure sheaf. J. Reine Angew. Math. , 519:73--95, 2000

work page 2000

[19] [19]

6- F unctor F ormalisms and S mooth R epresentations, 2024

Claudius Heyer and Lucas Mann. 6- F unctor F ormalisms and S mooth R epresentations, 2024

work page 2024

[20] [20]

A generalization of formal schemes and rigid analytic varieties

Roland Huber. A generalization of formal schemes and rigid analytic varieties. Math. Z. , 217(4):513--551, 1994

work page 1994

[21] [21]

\' E tale cohomology of rigid analytic varieties and adic spaces

Roland Huber. \' E tale cohomology of rigid analytic varieties and adic spaces . Aspects of Mathematics, E30. Friedr. Vieweg & Sohn, Braunschweig, 1996

work page 1996

[22] [22]

Kedlaya, David Hansen, Bastian Haase, Shizhang Li, Ruochuan Liu, Peter Scholze, Annie Carter, Zonglin Jiang, Jake Postema, Daniel Aaron Smith, Claus Mazanti Sorensen, and Xin Tong

Kiran S. Kedlaya, David Hansen, Bastian Haase, Shizhang Li, Ruochuan Liu, Peter Scholze, Annie Carter, Zonglin Jiang, Jake Postema, Daniel Aaron Smith, Claus Mazanti Sorensen, and Xin Tong. Sheaves, stacks, and shtukas. Perfectoid Spaces , 2019

work page 2019

[23] [23]

Kottwitz

Robert E. Kottwitz. Isocrystals with additional structure. II . Compos. Math. , 109(3):255--339, 1997

work page 1997

[24] [24]

Higher topos theory , volume 170 of Ann

Jacob Lurie. Higher topos theory , volume 170 of Ann. Math. Stud. Princeton, NJ: Princeton University Press, 2009

work page 2009

[25] [25]

Higher algebra

Jacob Lurie. Higher algebra. 2017

work page 2017

[26] [26]

The 6-functor formalism for z_ - and q_ -sheaves on diamonds

Lucas Mann. The 6-functor formalism for Z _ - and Q _ -sheaves on diamonds. https://arxiv.org/abs/2209.08135, 2022

work page arXiv 2022

[27] [27]

A p - A dic 6- F unctor F ormalism in R igid- A nalytic G eometry

Lucas Mann. A p -adic 6- F unctor F ormalism in R igid- A nalytic G eometry. https://arxiv.org/abs/2206.02022, 2022

work page arXiv 2022

[28] [28]

On locally analytic vectors of the completed cohomology of modular curves

Lue Pan. On locally analytic vectors of the completed cohomology of modular curves. Forum of Mathematics, Pi , 10:e7, 2022

work page 2022

[29] [29]

On locally analytic vectors of the completed cohomology of modular curves II

Lue Pan. On locally analytic vectors of the completed cohomology of modular curves II . https://arxiv.org/abs/2209.06366, 2022

work page arXiv 2022

[30] [30]

Geometric S en theory over rigid analytic spaces, 2023

Juan Esteban Rodr\'iguez Camargo. Geometric S en theory over rigid analytic spaces, 2023

work page 2023

[31] [31]

The analytic de rham stack in rigid geometry

Juan Esteban Rodr\'iguez Camargo. The analytic de rham stack in rigid geometry. https://arxiv.org/abs/2401.07738, 2024

work page arXiv 2024

[32] [32]

Locally analytic completed cohomology, 2024

Juan Esteban Rodr\'iguez Camargo. Locally analytic completed cohomology, 2024

work page 2024

[33] [33]

Solid locally analytic representations of \(p\) -adic Lie groups

Joaqu \' n Rodrigues Jacinto and Juan Esteban Rodr \' guez Camargo. Solid locally analytic representations of \(p\) -adic Lie groups. Represent. Theory , 26:962--1024, 2022

work page 2022

[34] [34]

Solid locally analytic representations

Joaqu\'in Rodrigues Jacinto and Juan Esteban Rodr\'iguez Camargo. Solid locally analytic representations. https://arxiv.org/abs/2305.03162, 2023

work page internal anchor Pith review Pith/arXiv arXiv 2023

[35] [35]

Towards a theory of local S himura varieties

Michael Rapoport and Eva Viehmann. Towards a theory of local S himura varieties. M\"unster J. Math. , 7(1):273--326, 2014

work page 2014

[36] [36]

Rapoport and Th

M. Rapoport and Th. Zink. Period spaces for p -divisible groups , volume 141 of Annals of Mathematics Studies . Princeton University Press, Princeton, NJ, 1996

work page 1996

[37] [37]

p -adic H odge theory for rigid-analytic varieties

Peter Scholze. p -adic H odge theory for rigid-analytic varieties. Forum Math. Pi , 1:e1, 77, 2013

work page 2013

[38] [38]

On the p -adic cohomology of the L ubin- T ate tower

Peter Scholze. On the p -adic cohomology of the L ubin- T ate tower. Ann. Sci. \' E c. Norm. Sup\' e r. (4) , 51(4):811--863, 2018. With an appendix by Michael Rapoport

work page 2018

[39] [39]

Etale cohomology of diamonds

Peter Scholze. Etale cohomology of diamonds. https://arxiv.org/abs/1709.07343v3, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022

[40] [40]

Algebras of p -adic distributions and admissible representations

Peter Schneider and Jeremy Teitelbaum. Algebras of p -adic distributions and admissible representations. Invent. Math. , 153(1):145--196, 2003

work page 2003

[41] [41]

Moduli of p -divisible groups

Peter Scholze and Jared Weinstein. Moduli of p -divisible groups. Camb. J. Math. , 1(2):145--237, 2013

work page 2013

[42] [42]

Berkeley Lectures on p-adic Geometry: (AMS-207)

Peter Scholze and Jared Weinstein. Berkeley Lectures on p-adic Geometry: (AMS-207) . Princeton University Press, 2020

work page 2020

[43] [43]

A motivic version of the theorem of F ontaine and W intenberger

Alberto Vezzani. A motivic version of the theorem of F ontaine and W intenberger. Compos. Math. , 155(1):38--88, 2019

work page 2019