Generalization of Deuring Reduction Theorem

2012/09/24 by Zaytsev, Alexey
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1209.5207

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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