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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).

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  1. Dipartimento di Matematica, 2a Università di Roma “Tor Vergata”, 00133, Rome, Italy

    René Schoof

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  1. René Schoof
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Correspondence to René Schoof.

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Schoof, R. Semistable abelian varieties with good reduction outside 15. manuscripta math. 139, 49–70 (2012). https://doi.org/10.1007/s00229-011-0509-y

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