##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Adrian Iovita

#### Concordia Univ., Montreal

## A p-adic criterion for good reduction of curves over a p-adic field

##### Abstract:

If A is an abelian variety over a p-adic field K then A has good reduction if and only if the p-adic Tate module of A is a crystalline representation of the absolute Galois group of K. As there are examples of curves over K with bad reduction whose Jacobian has good reduction, the Galois action on the p-adic etale cohomology of the curve does not determine its reduction. We will discuss these issues and point to a p-adic criterion of good reduction for curves.

Host: Cristian Popescu

### February 18, 2011

### 3:00 PM

### AP&M 6402

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