Bad reduction of genus $3$ curves with complex multiplication
Number Theory
2014-12-11 v2 Algebraic Geometry
Abstract
Let be a smooth, absolutely irreducible genus- curve over a number field . Suppose that the Jacobian of has complex multiplication by a sextic CM-field . Suppose further that contains no imaginary quadratic subfield. We give a bound on the primes of such that the stable reduction of at contains three irreducible components of genus .
Keywords
Cite
@article{arxiv.1407.3589,
title = {Bad reduction of genus $3$ curves with complex multiplication},
author = {Irene Bouw and Jenny Cooley and Kristin Lauter and Elisa Lorenzo Garcia and Michelle Manes and Rachel Newton and Ekin Ozman},
journal= {arXiv preprint arXiv:1407.3589},
year = {2014}
}