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Hodge tate period map

NettetThe Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G (A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G (Q_p) and can be thought of as a p-adic analogue ... Nettet23. mar. 2024 · Download PDF Abstract: Consider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime p>3. Consider its perfectoid cover …

On two mod p period maps: Ekedahl–Oort and fine Deligne

NettetConjecture (Hodge Conjecture) The cycle class map cl is surjective. A cohomology class in Hj;j dR (V(C)) \H 2j B (V(C);Q) i.e, a class of type (j;j) with rational periods is called … NettetNext, we give an explicit description of the restriction of Scholze’s Hodge–Tate period map πHT [Sch15, §3.3] to the Tate curve parameter spaces. Recall that over the ordinary locus, the kernel of the Hodge–Tate map TpE→ ωEis the Tate module TpCof the canonical p-divisible subgroup, and thus the Hodge–Tate filtration is given by ... how to remove grease from leather https://gpfcampground.com

The Hodge and Tate conjectures: some numerical experiments.

Nettet25. feb. 2024 · 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 module and the Faltings extension, which was already used in the original proof. Then, we construct overconvergent Eichler-Shimura (ES) … NettetHodge-Tate decompositions for Siegel varieties [ PDF] In this talk we will sketch a new proof of the Hodge-Tate decompositions for the proétale cohomology of Siegel varieties. The idea behind is to apply the BGG method of Faltings via the Hodge-Tate period map and the infinite level Siegel variety. ANTONIO CAUCHI, Concordia University. NettetThus, we prove new results on the p-adic geometry of Shimura varieties (of Hodge type). Namely, the Shimura varieties become perfectoid when passing to the inverse limit over all levels at p, and a new period map towards the flag variety exists on them, called the Hodge-Tate period map. It is roughly analogous to the embedding of the hermitian how to remove grease from kitchen hood

Cusps and -ExpansionPrinciples for Modular Curves at Infinite Level

Category:[2102.13099] p-adic Eichler-Shimura maps for the modular curve

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Hodge tate period map

Hodge theory and period maps (Fall 2024) Home page Eduard …

NettetHodge theory and period maps (Fall 2024) This course will be taught fully online. I will produce handwritten course notes, posted here (last update Nov 30). My intention is to … NettetThe idea of our construction can be stated very naively using the geometry of the Hodge-Tate period map. We fix a prime-to-?level?(a compact open subgroup of GL2(A (?) 5)) and write: 1. -/C?for the perfectoid compactified modular curve of prime-to-?level?and infinite level at ? 2. Ifor the ideal sheaf of the boundary (cusps) on -

Hodge tate period map

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NettetThe Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G(A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G(Q_p) and can be thought of as a p-adic analogue of … 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 …

http://davidrenshawhansen.com/periodmapmod.pdf Nettet31. 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 …

Finally, 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 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 …

Nettetthe Hodge-Tate period map for Hodge type Shimura varieties (which was then refined in [CS15]). More precisely, let S KpK p be a Hodge-type Shimura variety at some levelK …

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 … nord wsa fbNettetThe 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. nord x cartridgeNettetorbit in the period domain of Hodge-Tate structures convergesto a semistable point (filtration) in the period domain of the p-adic Hodge structure. Furthermore, the nilpotent orbits of the limit point are asymptotic to the twisted period map [Theorem 3.2]. Therefore, the orbit theorems come with some estimates on the nord with tomatoNettetag 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 ... how to remove grease from laptop keyboardhttp://www.davidrenshawhansen.com/owr-report-hansenaug2016.pdf how to remove grease from machineryNettetThe Hodge-Tate spectral sequences play an important role in some of the recent breakthroughs in arithmetic geometry, namely it is used to de ne Hodge-Tate period … how to remove grease from laptop touchpadNettetspaces with grading-preserving maps (p141). Hodge-Tate representations are stable under duality, tensor product, direct sum, and passage to submodules and quotients. … how to remove grease from metal