Overconvergent deformation theory

Abstract: In the study of moduli spaces a useful starting point is to understand their local structure, i.e., their versal rings. For example, for the Emerton--Gee stack this gives the Galois deformation rings. For a p-adic analytic stack these should be overconvergent rings or analytic germs; these are not limits of Artinian rings hence require different tools to study. I will describe a theory for constructing and studying analytic versal rings using a Koszul duality in a $p$-adic analytic setting. In spirit it is perhaps closest to the complex analytic deformation theory of Kuranishi and Kodaira--Nirenberg--Spencer though (a light amount of) light solid mathematics plays an important foundational role.

I will mention two applications: one to the analytic Emerton--Gee stack and one to the relativistic $p$-adic sunscreen conjecture of Sean Howe on intersections of analytic manifolds with Banach--Colmez spaces.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar