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Applications of an Equivariant Etale Cohomology to Arithmetic Topology

Baptiste Morin
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Abstract

A. Sikora has shown 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.

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Baptiste Morin. 2006-02-03. Applications of an Equivariant Etale Cohomology to Arithmetic Topology. https://arxiv.org/abs/math/0602064

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