On the Weil-étale cohomology of number fields

Details On the Weil-étale cohomology of number fields On the Weil-étale cohomology of number fields

2010-06-02

arxiv.org/abs/1006.0521v1

Mathematics

Number Theory

50 pages. To appear in Trans. Amer. Math. Soc

Scientific paper

We give a direct description of the category of sheaves on Lichtenbaum's
Weil-\'etale site of a number ring. Then we apply this result to define a
spectral sequence relating Weil-\'etale cohomology to Artin-Verdier \'etale
cohomology. Finally we construct complexes of \'etale sheaves computing the
expected Weil-\'etale cohomology.

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