Semistable abelian Varieties over Q
数论
2007-05-23 v1 代数几何
摘要
We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer--Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with good reduction outside primes dividing N precisely when N is not in the set {1,2,3,5,6,7,10,13}.
引用
@article{arxiv.math/0311365,
title = {Semistable abelian Varieties over Q},
author = {Frank Calegari},
journal= {arXiv preprint arXiv:math/0311365},
year = {2007}
}
备注
24 pages, to appear in Manuscripta Mathematica