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

C. S. Rajan

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arXiv · math/0209219

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

C. S. Rajan

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Abstract

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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C. S. Rajan. 2003-02-22. On the vanishing of the measurable Schur cohomology groups of Weil groups. https://arxiv.org/abs/math/0209219

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