Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
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Etale cohomology of diamonds
10 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Motivated by problems on the \'etale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the \'etale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic $p$. Using a natural functor from analytic adic spaces over $\mathbb Z_p$ to diamonds which identifies \'etale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book.
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UNVERDICTED 10representative citing papers
The category of pro-étale vector bundles on a proper rigid-analytic variety X over C is equivalent to the category of Higgs bundles on the eh-site of X.
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
Proves classicality for Hecke characters in completed cohomology of Hilbert modular varieties under absolute irreducibility and regular parallel weight conditions on Galois representations, giving new cases of the LCFM conjecture.
Proves relative p-adic monodromy theorem over dense open set and equivalence to Newton polygon constancy near rank-1 points for de Rham local systems, plus extension of conjecture to Newton partition interiors.
Proves independence of locally analytic vectors from G and G_b actions in dual infinite-level local Shimura varieties and deduces commutation properties for the p-adic Jacquet-Langlands functor plus isomorphism of de Rham cohomologies.
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.
Computes the geometric Sen operator on arbitrary Shimura varieties via equivariant bundles and the Hodge-Tate period map, yielding rational vanishing of completed cohomology.
On perfectoid spaces over p-adic fields, étale and v-topological G-torsors coincide for arbitrary rigid analytic groups G, generalizing prior results for Ga and GL_n, with applications to generalized Q_p-representations equaling v-vector bundles.
Proves a deformation theorem for prismatic higher (G,μ)-displays over quasi-syntomic rings, extends p-divisible group classification, and relates the display stack to integral local Shimura varieties.
citing papers explorer
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On a conjecture of Pappas and Rapoport
Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
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Igusa Stacks and the Cohomology of Shimura Varieties
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
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Classicality of Hilbert modular forms
Proves classicality for Hecke characters in completed cohomology of Hilbert modular varieties under absolute irreducibility and regular parallel weight conditions on Galois representations, giving new cases of the LCFM conjecture.
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p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy
Proves relative p-adic monodromy theorem over dense open set and equivalence to Newton polygon constancy near rank-1 points for de Rham local systems, plus extension of conjecture to Newton partition interiors.
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A Jacquet-Langlands functor for $p$-adic locally analytic representations
Proves independence of locally analytic vectors from G and G_b actions in dual infinite-level local Shimura varieties and deduces commutation properties for the p-adic Jacquet-Langlands functor plus isomorphism of de Rham cohomologies.
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Relative representability and parahoric level structures
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.
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Locally analytic completed cohomology
Computes the geometric Sen operator on arbitrary Shimura varieties via equivariant bundles and the Hodge-Tate period map, yielding rational vanishing of completed cohomology.
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Deformations of Prismatic Higher $(G,\mu)$-Displays over Quasi-Syntomic Rings
Proves a deformation theorem for prismatic higher (G,μ)-displays over quasi-syntomic rings, extends p-divisible group classification, and relates the display stack to integral local Shimura varieties.