Manuscripta Mathematica

, Volume 139, Issue 1, pp 49–70

Semistable abelian varieties with good reduction outside 15

Article

DOI: 10.1007/s00229-011-0509-y

Cite this article as:
Schoof, R. manuscripta math. (2012) 139: 49. doi:10.1007/s00229-011-0509-y

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 X0(15).

Mathematics Subject Classification (2000)

11GXX11R3714KXX14L15

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica2a Università di Roma “Tor Vergata”RomeItaly