The p-adic Geometric Langlands Correspondence

The p-adic Geometric Langlands Correspondence

Thu, 10/05/2012
15:00 		Alex Paulin (University of Nottingham) Representation Theory Seminar Add to calendar L3
The p-adic Geometric Langlands Correspondence
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) $.