EVENT DETAILS AND ABSTRACT

Title: The monodromy of simple surface singularities in mixed characteristic
Speaker: Jason Kountouridis
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

Given a smooth proper surface X over a $p$-adic field, it is a generally open problem in arithmetic geometry to relate the mod $p$ reduction of X with the monodromy action of inertia on the $\ell$-adic cohomology of X, the latter viewed as a Galois representation ($\ell \neq p$). In this talk, I will focus on the case of X degenerating to a surface with simple singularities, also known as rational double points. This class of singularities is linked to simple simply-laced Lie algebras, which in turn allows for a concrete description of the associated local monodromy. Along the way we will discuss a mixed-characteristic analogue of some classical results of Brieskorn-Slodowy and Borho-MacPherson, regarding Grothendieck-Springer simultaneous resolutions and Springer representations.