Speaker:  Vadim Vologodsky (Institute for Advanced Study)

 In-Person and Virtual

Zoom         https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09

Title:          On the de Rham cohomology of the local system P^{1/h}

Abstract:  Let X -->S be a smooth family of algebraic varieties, P an invertible function on X. Consider the relative de Rham cohomology of the asymptotic D-module   P^{1/h}: = (O_X, hd + dP/P). In the limit, when h goes to 0, the cohomology  depends only on the neighborhood of the critical locus of function P. I will explain how, when  working with algebraic varieties over Z/nZ, the above "asymptotic" formula for the cohomology becomes exact. I will also explain some applications to the study of the KZ equations over Z/nZ. The talk is based on a joint work with Alexander Varchenko.