Étale cohomology and reduction of abelian varieties

A. Silverberg; Yu. G. Zarhin

Bulletin de la Société Mathématique de France (2001)

  • Volume: 129, Issue: 1, page 141-157
  • ISSN: 0037-9484

Abstract

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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.

How to cite

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Silverberg, A., and Zarhin, Yu. G.. "Étale cohomology and reduction of abelian varieties." Bulletin de la Société Mathématique de France 129.1 (2001): 141-157. <http://eudml.org/doc/272465>.

@article{Silverberg2001,
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.},
author = {Silverberg, A., Zarhin, Yu. G.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {abelian varieties; semistable reduction; étale cohomology; monodromy},
language = {eng},
number = {1},
pages = {141-157},
publisher = {Société mathématique de France},
title = {Étale cohomology and reduction of abelian varieties},
url = {http://eudml.org/doc/272465},
volume = {129},
year = {2001},
}

TY - JOUR
AU - Silverberg, A.
AU - Zarhin, Yu. G.
TI - Étale cohomology and reduction of abelian varieties
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 1
SP - 141
EP - 157
AB - 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.
LA - eng
KW - abelian varieties; semistable reduction; étale cohomology; monodromy
UR - http://eudml.org/doc/272465
ER -

References

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  12. [12] —, « Semistable reduction of abelian varieties over extensions of small degree », J. Pure Appl. Algebra 132 (1998), no. 2, p. 179–193. Zbl0938.11029MR1640087
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