Displaying similar documents to “Cohomology of the boundary of Siegel modular varieties of degree two, with applications”

Étale cohomology and reduction of abelian varieties

A. Silverberg, Yu. G. Zarhin (2001)

Bulletin de la Société Mathématique de France

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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.