Geometric Langlands Seminar, November 2020

During November 2020, Bhargav Bhatt will give a series of lectures over Zoom in the Geometric Langlands Seminar at UChicago.

The seminar meets at 4:10pm Chicago time on Mondays, starting November 2.

Please email me at amathew (at) math (dot) uchicago (dot) edu for the Zoom coordinates.

Title: A p-adic Riemann-Hilbert functor and applications


The goal of these talks is two-fold.

First, I'll discuss a p-adic Riemann-Hilbert functor that attaches coherent objects to constructible F_p-sheaves on algebraic varieties over an algebraically closed p-adic field; I'll especially focus on the good behaviour of this functor with respect to the perverse t-structure. (This is joint work in progress with Jacob Lurie.)

Secondly, I'll discuss a variant of the Kodaira vanishing theorem in mixed characteristic algebraic geometry as well as some applications. This result relies on two ingredients: the Riemann-Hilbert functor mentioned above to almost solve the problem, and then (log) prismatic cohomology to pass from an almost solution to an honest solution.