Applications of an Equivariant Etale Cohomology to Arithmetic Topology
Number Theory
2010-06-04 v3 Algebraic Geometry
Algebraic 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.
Keywords
Cite
@article{arxiv.math/0602064,
title = {Applications of an Equivariant Etale Cohomology to Arithmetic Topology},
author = {Baptiste Morin},
journal= {arXiv preprint arXiv:math/0602064},
year = {2010}
}
Comments
This is the final version published in Compositio Math. 144 (2008), no. 1, 32-60