  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.
