## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** p-adic Geometric Class Field Theory

**Speaker:** Alexander Paulin

**Speaker Info:** Berkeley

**Brief Description:**

**Special Note**: **There will not be a pre-seminar talk this week.**

**Abstract:**

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

**Time:** 3:00PM

**Where:** Lunt 104

**Contact Person:** Ellen Eischen

**Contact email:** eeischen@math

**Contact Phone:** 847-467-1891

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