Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés / Jean-Loup Waldspurger

This paper, a book in its own right, is devoted to clarifying two of the central questions which one encounters in trying to exploit the trace formula. Let G be an unramified classical group defined over a non-archimedean local field of characteristic 0 and residual characteristic p which is assumed to avoid an explicit finite set. Let g be its Lie algebra over F; the object which is investigated here is the set of stably invariant distributions on g which are supported on the set of nilpotent elements. This is achieved on p. 308. Let now H be an elliptic unramified endoscopic group of G. The second major result of the paper describes explicitly a transfer operator from the corresponding set of distributions for H to those for G. The analysis in this paper is primarily local in nature; it is very delicate and intricate with many subsidiary results, which the reviewer cannot hope to summarize here. (Zentralblatt)

Bibliogr. p. [447]-449. Index