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
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