Applications of an Equivariant Etale Cohomology to Arithmetic Topology

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.

arXiv commentThis is the final version published in Compositio Math. 144 (2008), no. 1, 32-60