STNB 2015 (29th year)
Bad reduction of genus 3 curves with complex multiplication
Presenters
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 $\mathfrak{p}$ of $M$ such that the stable reduction of $C$ at $\mathfrak{p}$ contains three irreducible componentsof genus $1$.
Joint work with Bouw, Cooley, Lauter, Manes, Newton, Ozman.
Files
Account
Languages: