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Tamagawa numbers and semisimple groups (after Kottwitz). (Nombres de Tamagawa des groupes semi-simples (d’après Kottwitz).) (French) Zbl 0705.11028
Sémin. Bourbaki, Vol. 1988/89, 41e année, Exp. No. 702, Astérisque 177-178, 61-82 (1989).
This is a report on the recently completed proof of Weil’s conjecture about Tamagawa numbers. Discussed at length are the methods of the paper of R. Kottwitz [Ann. Math. (2) 127, 629–646 (1988; Zbl 0678.22012)] and the main theorem of this paper, that the Tamagawa number is invariant under inner twisting. The report thus serves as an introduction to Langlands’ notion of stable trace formula.
For the entire collection see [Zbl 0691.00001].
Reviewer: Diana Shelstad
MSC:
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11E72 Galois cohomology of linear algebraic groups
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings