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On the geometrization of the $p$-adic local Langlands correspondence

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Pierre Colmez, Gabriel Dospinescu, Wies{l}awa Nizio{l}

Number Theory · Submitted 5 Aug 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$.

how it is stated · asserted 0.77 read the record →

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arXiv ID2408.02358 (version 2)
Pith IDOLNO4DYP, Pith's permanent record of this paper and its review
CitationGabriel Dospinescu, Pierre Colmez, Wies{\l}awa Nizio{\l}. "On the geometrization of the $p$-adic local Langlands correspondence." arXiv:2408.02358 (2024). https://pith.science/paper/OLNO4DYP
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,644 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$. contribution 0.98 0.66 0.30 asserted 0.77

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.88.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 4 sentences without a confident label

Cites as background 3 papers
  • 1mm $∙$ Emerton (2008) proved in [ref] big parts of his local-global compatibility conjecture; this was later revisited and complemented by Caraiani-Emerton-Gee-Geraghty--Shin [ref] , Pan [ref] , Colmez-Wang [ref] .

    Une factorisation de la cohomologie compl\'et\'ee et du syst\`eme de Beilinson-Kato · Some history · 0.89

  • 1mm $∙$ Emerton (2008) proved in [ref] big parts of his local-global compatibility conjecture; this was later revisited and complemented by Caraiani-Emerton-Gee-Geraghty--Shin [ref] , Pan [ref] , Colmez-Wang [ref] .

    Exercices ad\'eliques · Some history · 0.89

  • 1mm $∙$ Emerton-Gee-Hellmann (2022) formulated in [ref] a general categorification conjecture.

    2210.01404 · Other groups · 0.96

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