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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on good reduction of simple Abelian varieties
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by C. Adimoolam PDF
Proc. Amer. Math. Soc. 64 (1977), 196-198 Request permission

Abstract:

In this note it is shown that the reduction of a simple abelian variety of dimension $\geqslant 2$, defined over an algebraic number field, at any finite good prime need not be simple. We give an example of a two-dimensional simple abelian variety defined over an algebraic number field whose reduction at any finite prime is isogenous either to a product of ordinary elliptic curves or to a product of supersingular elliptic curves.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 196-198
  • MSC: Primary 14K15; Secondary 14G25
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0447259-X
  • MathSciNet review: 0447259