A stable trace formula. II: Global descent. (English) Zbl 0978.11025
This is the second paper in the series dealing with the problem of stabilization of the global trace formula for a general connected group. Let us consider a connected reductive group \(G\) over a number field \(F\). The trace formula of \(G\) is the identity obtained from the geometric and spectral expansions of a certain linear form \(I(f)\) in terms of distributions parametrized by conjugacy classes \(\gamma\) or representations \(\pi\) of the Levi subgroup \(M\), respectively, with the coefficients \(a^M(\gamma)\) or \(a^M(\pi)\). The geometric coefficients or more fundamental “elliptic” coefficients \(a_{\text{ell}}^G\), in terms of which the coefficients \(a^M(\gamma)\) are defined, are the key focus of the present work. The author studies a descent formula for \(a_{\text{ell}}^G\) and discusses the descent theorem of Langlands and Shelstad. He also establishes the global descent mapping.
For Part I, see Doc. Math., J. DMV Extra Vol. ICM Berlin 1998, Vol. II, 507-517 (1995; Zbl 0973.11057)].
For Part I, see Doc. Math., J. DMV Extra Vol. ICM Berlin 1998, Vol. II, 507-517 (1995; Zbl 0973.11057)].
Reviewer: Eugene Kryachko (Kyïv)
MSC:
11F72 | Spectral theory; trace formulas (e.g., that of Selberg) |
22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |
11R39 | Langlands-Weil conjectures, nonabelian class field theory |
22E50 | Representations of Lie and linear algebraic groups over local fields |
11F70 | Representation-theoretic methods; automorphic representations over local and global fields |