Seminar series
Date
Wed, 26 Sep 2012
Time
09:15 -
10:15
Location
L1
Speaker
Glenn Stevens
Organisation
Boston University
Using Faltings' theory of the Hodge-Tate sequence of an abelian scheme we construct certain sheaves $\Omega^\kappa$, where $\kappa$ is a not-necessarily integral weight, over formal subschemes of modular varieties over which the canonical subgroup exists. These sheaves generalize the integral powers, $\omega^k$, of the sheaf $\omega$ of relative differentials on a modular curve. Global sections of $\Omega^\kappa$ provide geometric realizations of overconvergent automorphic forms of non-integral weight. Applications of this approach to the theory of $p$-adic Hilbert modular forms will be given. This is joint work with Fabrizio Andreotti and Adrian Iovita.