, Volume 139, Issue 1-2, pp 49-70
Date: 07 Dec 2011

Semistable abelian varieties with good reduction outside 15

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Abstract

We show that there are no non-zero semi-stable abelian varieties over \({{\bf Q}(\sqrt{5})}\) with good reduction outside 3 and we show that the only semi-stable abelian varieties over Q with good reduction outside 15 are, up to isogeny over Q, powers of the Jacobian of the modular curve X 0(15).