##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## David Kohel

#### University of Sydney

## Constructive $p$-adic $CM$ for genus $2$ curves

##### Abstract:

Canonical lifts of elliptic curves have been used both for point counting (determining the zeta function) and for constructing $CM$ invariants. In genus $2$, Mestre introduced an algorithm for determining the zeta function of a curve using canonical lifts. In this talk I will describe an algorithm for determining $CM$ invariants in the moduli space of genus $2$ curves.

Host: W. Stein

### September 29, 2005

### 2:00 PM

### AP&M 7321

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