##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Tamas Szamuely

#### UPenn and The Renyi Institute of Mathematics (Hungarian Academy of Science)

## On the arithmetic of $1$--motives

##### Abstract:

$1$--motives have been introduced by Deligne in the 1970s as the simplest kind of mixed motives; basically, they are the only ones having a simple and concrete geometric description. In recent years there has been a resurgence of interest in them, and they have been successfully applied to arithmetic questions as well, such as generalizations of the classical duality theorems of Poitou and Tate, or finding rational points on algebraic varieties. I shall explain some of these results.

Host: Cristian Popescu

### December 2, 2010

### 1:00 PM

### AP&M 7321

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