The Hodge-Tate sequence and overconvergent $p$-adic modular sheaves

26 September 2012
Glenn Stevens
<p>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. &nbsp; These sheaves generalize the integral powers, $\omega^k$, of the sheaf $\omega$ of relative differentials on a modular curve. &nbsp; Global sections of $\Omega^\kappa$ provide geometric realizations of overconvergent automorphic forms of non-integral weight. &nbsp;Applications of this approach to the theory of $p$-adic Hilbert modular forms will be given. &nbsp; This is joint work with Fabrizio Andreotti and Adrian Iovita.</p>
  • Number Theory Seminar