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arXiv · 1209.5207

Generalization of Deuring Reduction Theorem

Alexey Zaytsev
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Abstract

In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM field $K$ over a number field at a pace of good reduction. We establish a connection between a decomposition of the first truncated Barsotti-Tate group scheme $A[p]$ and a decomposition of $p\cO_{K}$ into prime ideals. In particular, we produce these explicit relationships for Abelian varieties of dimensions $1, 2$ and 3.

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Alexey Zaytsev. 2012-09-24. Generalization of Deuring Reduction Theorem. https://arxiv.org/abs/1209.5207

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