Local Points on P -adically Uniformized Shimura Varieties
نویسندگان
چکیده
Using the p-adic uniformization of Shimura varieties we determine, for some of them, over which local fields they have rational points. Using this we show in some new curve cases that the jacobians are even in the sense of [PS].
منابع مشابه
P -adic Uniformization of Unitary Shimura Varieties Ii
In this paper we show that certain Shimura varieties, uniformized by the product of complex unit balls, can be p-adically uniformized by the product (of equivariant coverings) of Drinfeld upper half-spaces and their equivariant coverings. We also extend a p-adic uniformization to automorphic vector bundles. It is a continuation of our previous work [V] and contains all cases (up to a central mo...
متن کاملWEIGHT-MONODROMY CONJECTURE FOR p-ADICALLY UNIFORMIZED VARIETIES
The aim of this paper is to prove the weight-monodromy conjecture (Deligne’s conjecture on the purity of monodromy filtration) for varieties with p-adic uniformization by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply an argument of Steenbrink, M. Saito to the weight spectral sequence of Rapop...
متن کاملPolarization Measurement aboard the Satellite and Solution of the Emission Mechanism of the Gamma-Ray Bursts
Tetsushi Ito (Kyoto University, Graduate School of Science, Assistant Professor) 【Outline of survey】 Shimura varieties are algebraic varieties (geometric objects defined by equations), which are generalizations of modular curves. Previously, several mathematical objects in arithmetic geometry, Galois representations, automorphic representations were studied from individual perspectives. However...
متن کاملP -adic Uniformization of Unitary Shimura Varieties
Introduction Let Γ ⊂ PGUd−1,1(R) 0 be a torsion-free cocompact lattice. Then Γ acts on the unit ball B ⊂ C by holomorphic automorphisms. The quotient Γ\B is a complex manifold, which has a unique structure of a complex projective variety XΓ (see [Sha, Ch. IX, §3]). Shimura had proved that when Γ is an arithmetic congruence subgroup, XΓ has a canonical structure of a projective variety over some...
متن کاملShimura Varieties with Parahoric Level
This survey article is intended to introduce the reader to several important concepts relating to Shimura varieties with parahoric level structure at p. The main tool is the Rapoport-Zink local model [RZ], which plays an important role in several aspects of the theory. We discuss local models attached to general linear and symplectic groups, and we illustrate their relation to Shimura varieties...
متن کامل