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