Étale cohomology and reduction of abelian varieties

Details Étale cohomology and reduction of abelian varieties Étale cohomology and reduction of abelian varieties

1998-08-29

arxiv.org/abs/math/9808125v2

Mathematics

Algebraic Geometry

Scientific paper

In this paper we study the \'etale 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 \'etale cohomology groups with finite coefficients.

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