CONSTRUCTION OF AUTOMORPHIC FORMS FOR AMPLE FACTORS OF QUASI-ABELIAN VARIETIES

Automorphic Forms on Shimura Varieties

Hyperbolicity, automorphic forms and Siegel modular varieties

We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an étale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel modular varieties, we improve some former results of Nadel on the non-existence of certain level structures on abelian varieties over complex function fields.

On Mumford’s Construction of Degenerating Abelian Varieties

For a one-dimensional family of abelian varieties equipped with principal theta divisors a canonical limit is constructed as a pair consisting of a reduced projective variety and a Cartier divisor on it. Properties of such pairs are established.

Measures of Simultaneous Approximation for Quasi-periods of Abelian Varieties

Theorem 1.1 (Chudnovsky’s theorems). Let Λ = Zω+Zω′ ⊂ C be a lattice with invariants g2, g3, Weierstrass functions ℘, ζ and quasi-periods η, η′, all defined in the usual way (see [Sil94]). Each of the sets below contains at least two algebraically independent numbers : first (1) {g2, g3, η ω , π ω}, (2) {g2, g3, ω, η, ω′, η′}; if we assume g2, g3 ∈ Q̄ : (3) { η ω , π ω}, (4) {ω, ω′, η, η′}; and ...

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...