Abelian varieties over Q with bad reduction in one prime only
Number Theory
2007-05-23 v1
Abstract
Let l be a prime. We show that there do not exist any non-zero semi-stable abelian varieties over Q with good reduction outside l if and only if l=2, 3, 5, 7 or 13. We show that any semi-stable abelian variety over Q with good reduction outside l=11 is isogenous to a power of the Jacobian variety of the modular curve X_0(11). In addition we show that there do not exist any non-zero abelian varieties over Q with good reduction outside l acquiring semi-stable reduction at l over a tamely ramified extension if and only if l \le 5.
Keywords
Cite
@article{arxiv.math/0502356,
title = {Abelian varieties over Q with bad reduction in one prime only},
author = {Rene' Schoof},
journal= {arXiv preprint arXiv:math/0502356},
year = {2007}
}