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A note on good reduction of simple Abelian varieties

Author: C. Adimoolam
Journal: Proc. Amer. Math. Soc. 64 (1977), 196-198
MSC: Primary 14K15; Secondary 14G25
MathSciNet review: 0447259
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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 [Enhancements On Off] (What's this?)

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Keywords: Simple abelian variety, good reduction, <I>p</I>-rank of an abelian variety, Barsotti-Tate group, Dieudonn&#233; module, indefinite quaternion algebra, ordinary and supersingular elliptic curves
Article copyright: © Copyright 1977 American Mathematical Society