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On special values of theta functions of genus two

Ehud De ShalitEyal Z. Goren — 1997

Annales de l'institut Fourier

We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.

Tamely ramified Hida theory

Assaf GoldbergerEhud de Shalit — 2002

Annales de l’institut Fourier

Let J 1 be the Jacobian of the modular curve associated with Γ 1 ( N p ) , ( p , N ) = 1 and J 0 the one associated with Γ 1 ( N ) Γ 0 ( p ) . We study J 1 [ p - 1 ] as a Hecke and Galois-module. We relate a certain matrix of p -adic periods to the infinitesimal deformation of the U p -operator.

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