Interpolating p-adic cohomology theories

Event time: 
Monday, October 28, 2019 - 5:15pm
LOM 206
Bhargav Bhatt
Speaker affiliation: 
University of Michigan
Event description: 

Abstract: Integration of differential forms against cycles on a complex manifold helps relate de Rham cohomology to singular cohomology, which forms the beginning of Hodge theory. The analogous story for p-adic manifolds, which is the subject of p-adic Hodge theory, is richer due to a wider variety of available cohomology theories (de Rham, etale, crystalline, and more) and torsion phenomena. In this talk, I will give a bird’s eye view of this picture, guided by the recently discovered notion of prismatic cohomology (which was inspired by calculations in homotopy theory) that provides some cohesion to the story. Based on joint works with Morrow and Scholze.