Semistable abelian Varieties over Q

Details Semistable abelian Varieties over Q Semistable abelian Varieties over Q

2003-11-21

arxiv.org/abs/math/0311365v1

Mathematics

Number Theory

24 pages, to appear in Manuscripta Mathematica

Scientific paper

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}.

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