Hodge tate period map
Nettet5. Perfectoid Shimura varieties and the Hodge-Tate period morphism 37 5.1. Siegel modular varieties with in nite level at pare perfectoid 37 6. Project description: The nilpotent ideal 48 References 49 1. Introduction One of the famous consequences of the Langlands program is the theorem that all elliptic curves over Q are modular [Wil95, … NettetIn mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre introduced and named Hodge–Tate structures using the results of Tate on …
Hodge tate period map
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Nettet2.8. Hodge{Tate decomposition40 2.9. Generic bers of p-divisible groups57 3. Period rings and functors60 3.1. Fontain’s formalism on period rings60 3.2. De Rham representations69 3.3. Properties of de Rham representations83 3.4. Crystalline representations93 References95 1. Introduction 1.1. A rst glimpse of p-adic Hodge … Nettetag variety exists on them, called the Hodge-Tate period map. It is roughly analogous to the embedding of the hermitian symmetric domain (which is roughly the inverse limit over all levels of the complex points of the Shimura variety) into its compact dual. The Hodge-Tate period map has several favorable properties, the most important being that ...
NettetThe first two parts of Theorem 12 are due to Scholze 5 Up to the precise identification of the target of the Hodge–Tate period morphism as the flag variety F ℓ G, μ \mathscr{F}\ell_{G,\mu} F ℓ G, μ in all cases, which is done in [16 A. Caraiani and P. Scholze, On the generic part of the cohomology of compact unitary Shimura varieties. Nettet8. nov. 2015 · The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing …
Nettet20. jun. 2024 · namely it is used to define Hodge-Tate period maps as in [Sch15], [CS17] and [CS19], which is. applied to prove the modularity theorem, and man y other important results in [ACC + 18]. NettetCareer. Georges Tate studied at the École normale supérieure de Fontenay-Saint-Cloud and received a doctorate in literature, then he taught history at the École Supérieure …
NettetConsider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime \(p\ge 5\).Consider its perfectoid cover \(S^{\text {ad}}(p^\infty )\) and the …
Nettetanalytic spaces, they are perfectoid, and admit a new kind of period map, called the Hodge–Tate period map, towards the flag variety. Moreover, the (semisimple) automorphic vector bundles come via pullback along the Hodge–Tate period map from the flag variety. In the case of the Siegel moduli space, the situation is fully analyzed … european wax center clifton njNettetFrom the Hodge-to-de Rham and the Hodge-Tate spectral sequence, one obtains abutments filtrations that we call the Hodge-de Rham filtration and the Hodge-Tate filtration. Their variation in families defines interesting period maps as we will recall in the next sections. 3. Period maps from de Rham cohomology european wax center cliftonNettetThey explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs … first american specialty insuranceNettet30. des. 2024 · We compute the p-torsion and p-adic étale cohomologies with compact support of period domains over local fields in the case of basic ... We give a new proof of Faltings's p-adic Eichler-Shimura decomposition of the modular curves via BGG methods and the Hodge-Tate period map. The key property is the relation between the Tate ... first americans to a new nation quizletFinally, let us explain the proof of the perversity result. Let be any compact Shimura variety of PEL type with hyperspecial level at . To motivate, recall two useful results for perverse sheaves in algebraic geometry: 1. Any simple perverse sheaf on a scheme of finite type is of the form for some locally closed subscheme and a … Se mer Recall our set-up. Let be a PEL datum of type A: 1. is a finite dimensional simple -algebra with center a CM field . 2. is positive involution of … Se mer Now let us come to the second main result, which asserts the "generic part" of the cohomology of our compact unitary Shimura varieties … Se mer european wax center clifton park nyNettet31. des. 1995 · Namely, the Shimura varieties become perfectoid when passing to the inverse limit over all levels at p, and a new period map towards the ag variety exists on them, called the Hodge-Tate period map. It is roughly analogous to the embedding of the hermitian symmetric domain (which is roughly the inverse limit over all levels of the … european wax center closterNettet4. nov. 2024 · The Hodge–Tate period map can be thought of as a p-adic analogue of the Borel embedding. However, unlike its complex counterpart, it is not injective, and the pushforward of the constant sheaf via the Hodge–Tate period map encodes interesting arithmetic information. first americans museum okc