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Utilisation d’une cohomologie étale équivariante en topologie arithmétique

Part of: (Co)homology theory Algebraic number theory: global fields

Published online by Cambridge University Press:  01 January 2008

Baptiste Morin
Baptiste Morin*
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France (email: Baptiste.Morin@math.u-bordeaux1.fr)
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Abstract

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Sikora has given results which confirm the analogy between number fields and 3-manifolds. However, he has given proofs of his results which are very different in the arithmetic and in the topological case. In this paper, we show how to provide a unified approach to the results in the two cases. For this we introduce an equivariant cohomology which satisfies a localization theorem. In particular, we obtain a satisfactory explanation for the coincidences between Sikora’s formulas which leads us to clarify and to extend the dictionary of arithmetic topology.

Keywords

étale cohomologylocalization theoremarithmetic topology

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 11R04: Algebraic numbers; rings of algebraic integers 11R32: Galois theory
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 1 , January 2008 , pp. 32 - 60
Copyright
Copyright © Foundation Compositio Mathematica 2008