Étale cohomology and reduction of abelian varieties

A. Silverberg; Yu G. Zarhin

doi:10.24033/bsmf.2389

Étale cohomology and reduction of abelian varieties

A. Silverberg, Yu G. Zarhin

Mathematics

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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.

Original language	English (US)
Pages (from-to)	141-157
Number of pages	17
Journal	Bulletin de la Societe Mathematique de France
Volume	129
Issue number	1
DOIs	https://doi.org/10.24033/bsmf.2389
State	Published - 2001

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Étale cohomology and reduction of abelian varieties

Abstract

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