Title: p-adic Geometric Class Field Theory
Speaker: Alexander Paulin
Speaker Info: Berkeley
Special Note: There will not be a pre-seminar talk this week.
Let X be a smooth projective complex curve. The (unramified) Geometric Langlands Correspondence asserts that to any irreducible rank n local system on X we may naturally associate a D-module on the moduli stack of rank n vector bundles over X. If we replace X with a smooth projective curve over a finite field of characteristic p and fix a prime l not equal to p, then we may restate the above correspondence in terms of l-adic local systems on X and l-adic perverse sheaves. The p-adic analogues of these objects are convergent isocrystals and arithmetic D-modules. In this lecture I'll show that there is a natural p-adic version of the Geometric correspondence in the Abelian case, suggesting the existence of a p-adic Geometric correspondence in general.Date: Monday, February 14, 2011