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Étale cohomology and reduction of abelian varieties

A. Silverberg·Yu. G. Zarhin
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Abstract

In this paper we study the étale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable over a quadratic extension) in terms of the action of the absolute inertia group on the étale cohomology groups with finite coefficients.

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A. Silverberg, Yu. G. Zarhin. 1999-11-02. Étale cohomology and reduction of abelian varieties. https://arxiv.org/abs/math/9808125

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