p-adic unit-root formulas and Dwork cohomology

par Masha Vlasenko (Institute of Mathematics of the Polish Academy of Sciences)

mardi 13 juin 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

We give a generalization of the Dwork congruences for a Laurent polynomial with one internal integral point in the Newton polytope to the case of arbitrary Laurent polynomial. Next, we consider crystals attached to a Laurent polynomial and draw a relation between our congruences and p-adic approximation to the Frobenius operator and the Gauss--Manin connection on it. This is work in progress jointly with Frits Beukers.