p-adic uniformization of unitary Shimura varieties

P -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...

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...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Height pairings on Shimura curves and p-adic uniformization

In a recent paper [16] of one of us it was shown that there is a close connection between the value of the height pairing of certain arithmetic 0-cycles on Shimura curves and the values at the center of their symmetry of the derivatives of certain metaplectic Eisenstein series of genus 2. On the one hand, the height pairing can be written as a sum of local height pairings. For example, if the 0...

Haruzo Hida ’ s p - adic automorphic forms on Shimura varieties

Three topics figure prominently in themodern higher arithmetic: zeta-functions, Galois representations, and automorphic forms or, equivalently, representations. The zeta-functions are attached to both the Galois representations and the automorphic representations and are the link that joins them. Although by and large abstruse and often highly technical the subject has many claims on the attent...