##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Michael Volpato

#### UCSD

## Counting superspecial abelian varieties

##### Abstract:

By invoking a result originally due to G. Shimura, we give a new proof of a generalization of a theorem of Deuring concerning supersingular elliptic curves, namely, a mass formula for superspecial abelian varieties with PEL-structures in characteristic p. This mass formula is then applied to estimate the dimension of Siegel modular cusp spaces modulo p and count the number of irreducible components in the supersingular region of the Siegel modular variety.

### January 15, 2009

### 1:00 PM

### AP&M 7321

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