Stable trace formula: Cuspidal tempered terms. (English) Zbl 0576.22020

Kottwitz, Robert E.

Duke Math. J. 51, 611-650 (1984).

Let G be a reductive group over a number field F. The meaning and the importance of a ”stable” trace formula for G are explained by R. P. Langlands in ”Les débuts d’une formule des traces stable” [Publ. Math. Univ. Paris VII, 13 (1983; Zbl 0532.22017)]. There he gives explicitly the stabilization of the regular elliptic part of the trace formula. In particular, he defines, for any elliptic endoscopic group H of G, a number \(\iota\) (G,H) relating the stable trace formula for H to the trace formula for G. In the present paper the author proves an identity for \(\iota\) (G,H) involving Tamagawa numbers. He uses this expression for \(\iota\) (G,H) in a ”speculative” consideration concerning the tempered cuspidal part of the trace formula and its stabilization.

Reviewer: J.G.M.Mars

MSC:

22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings
11F70	Representation-theoretic methods; automorphic representations over local and global fields
12G05	Galois cohomology

Keywords:

cohomology; reductive group; trace formula; elliptic endoscopic group; stable trace formula; Tamagawa numbers

Citations:

Zbl 0532.22017

References:

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