##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Alberto Minguez

#### Jussieu (University of Paris 6)

## Towards an l-modular Jacquet-Langlands correspondence

##### Abstract:

Let F be a non-Archimedean locally compact field of residue characteristic p, and let G be an inner form of GL(n,F), that is a group of the form GL(m,D) where D is a division algebra of centre F. Given R an algebraically closed field of characteristic different from p, I will explain how to classify the irreducible smooth representations of G with coefficients in R, in terms of parameters involving the supercuspidal representations of the Levi subgroups of G. We will discuss about the possibility of having a Jacquet-Langlands correspondence modulo $l$. This is a joint work with Vincent S$\mathrm{\acute{e}}$cherre.

Host: Wee Teck Gan

### April 22, 2010

### 2:00 PM

### AP&M 7321

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