##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Elisa Lorenzo Garcia

## Bad reduction of genus 3 curves with complex multiplication

##### Abstract:

Let C be a smooth, absolutely irreducible genus-3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1. Joint work with Bouw, Cooley, Lauter, Manes, Newton, Ozman.

Host: Kiran Kedlaya

### January 8, 2015

### 1:00 PM

### AP&M 7321

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