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In this paper we study theétale 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 thé etale cohomology groups with finite coefficients. Résumé (Cohomologieétale et réduction des variétés abéliennes) Nousétudions les groupes de cohomologiesétales associés auxdoi:10.24033/bsmf.2389 fatcat:jyvyjkmpjfh2pl4qrkrk3xp5g4