##### Department of Mathematics,

University of California San Diego

****************************

### Math 209 - Number Theory

## Rene Schoof

#### Universita di Roma Tor Vergata

## Finite group schemes and abelian varieties with good reduction outside one prime

##### Abstract:

The Jacobian $J_0(23)$ of the modular curve $X_0(23)$ is a semi-stable abelian variety over $\Bbb Q$ with good reduction outside $23$. It is simple. We prove that every simple semi-stable abelian variety over $\Bbb Q$ with good reduction outside $23$ is isogenous over $\Bbb Q$ to $J_0(23)$.

Host: Cristian Popescu

### April 16, 2015

### 2:00 PM

### AP&M 7321

****************************