Masha Vlasenko

Title: Atkin and Swinnerton-Dyer congruences for toric hypersurfaces

Abstract:
I will describe a realization of p-adic cohomology of an affine toric 
hypersurface which originates in Dwork's work. In a joint project with 
Frits Beukers we study Dwork crystals and related p-adic congruences 
for the coefficients of powers of a Laurent polynomial. As applications 
we get a congruence of the Atkin and Swinnerton--Dyer type and an explicit 
description of the unit-root subcrystal.