##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Krzystof Klosin

#### CUNY

## Modularity of Residually Reducible Galois Representations

##### Abstract:

Proving that Galois representations in many situations arise from automorphic forms has been a major theme in number theory for at least two decades. However, most of the existing work concerns the situation when the mod p reduction of the Galois representation (i.e., the residual representation) is irreducible and when the number field is totally real. We will present new modularity results for n-dimensional residually reducible Galois representations over arbitrary number fields. This is joint work with T. Berger.

Host: Cristian Popescu

### January 14, 2013

### 1:00 PM

### AP&M 6402

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