Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I

Abstract

For a field $F$ and a connected reductive group $G$ defined over $F$, we develop a theory of Kempf-Rousseau-Hesselink unipotent $F$-strata in $G(F)$ that should allow us to attack open problems in positive characteristic. As an application, we use this theory to establish the fine expansion of the unipotent contribution to the (non-twisted) trace formula over a global field of characteristic $p>0$. The unipotent $F$-strata play here the role of the unipotent geometric orbits in Arthur's work over a number field. The expansion in terms of products of local distributions is not discussed here; it will be the subject of further work.

139 pages, in French language

References in corpus (2)

• La formule des traces tordue pour les corps de fonctions
• Une mesure de Radon invariante sur les $F$-strates unipotentes

Cited by in corpus (1)

• Une mesure de Radon invariante sur les $F$-strates unipotentes