# The p-adic Geometric Langlands Correspondence

10 May 2012
15:00
Alex Paulin
Abstract

The geometric Langlands correspondence relates rank n integrable connections
on a complex Riemann surface $X$ to regular holonomic D-modules on
$Bun_n(X)$, the moduli stack of rank n vector bundles on $X$.  If we replace
$X$ by a smooth irreducible curve over a finite field of characteristic p
then there is a version of the geometric Langlands correspondence involving
$l$-adic perverse sheaves for $l\neq p$.  In this lecture we consider the
case $l=p$, proposing a $p$-adic version of the geometric Langlands
correspondence relating convergent $F$-isocrystals on $X$ to arithmetic
$D$-modules on $Bun_n(X)$.

• Representation Theory Seminar