On the vanishing of the measurable Schur cohomology groups of Weil groups

Details On the vanishing of the measurable Schur cohomology groups of Weil groups On the vanishing of the measurable Schur cohomology groups of Weil groups

2002-09-18

arxiv.org/abs/math/0209219v2

Mathematics

Number Theory

To appear in Compositio Mathematica. Minor editing, and a conjecture in the earlier version on the vanishing of the higher coh

Scientific paper

We generalize a theorem of Tate and show that the second cohomology of the Weil group of a global or local field with coefficients in $\C^*$ (or more generally, with coefficients in the complex points of a tori over $\C$) vanish, where the cohomology groups are defined using measurable cochains in the sense of Moore. We recover a theorem of Labesse proving that admissible homomorphisms of a Weil group to the Langlands dual of a reductive group can be lifted to an extension of the Langlands dual group by a tori.

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