Gyujin Oh : Moduli stack of isocrystals and counting local systems

Posted by Ronnie Nagloo , part of the Unlikely Intersections Seminar.

At

April 15, 2025, 2 p.m.

In

636 SEO

Abstract

For a smooth projective curve over a finite field, we construct the p-adic analytic moduli stack of isocrystals and study its geometry. This is a crystalline analogue of the moduli of integrable connections; in particular, it admits a Frobenius pullback endomorphism, even though the moduli space is a characteristic 0 object. We will illustrate, with the concrete example of rank 1 moduli, how its interesting geometry can be used to count (the p-adic analogues of) rank 1 local systems over a curve. Joint work with Koji Shimizu.