Stabilisation de la formule des traces tordue VIII: l'application epsilon_tilde{M} sur un corps de base local non-archim\'edien

It is a step in the proof of the stabilization of the twisted trace formula. We generalize to the twisted case the proposition 3.1 of the third Arthur's paper on the stabilization. That is, consider the difference between an omega-equivariant weighted orbital integral (relative to a Levi subspace of a twisted space) and its endoscopic avatar. Then this difference is the ordinary omega-orbital integral of some function on the Levi subspace. Here, the base-field is non-archimedean.Comment: in frenc

Les facteurs de transfert pour les groupes classiques: un formulaire

In the theory of endoscopy appears transfer factors. They were defined by Langlands and Shelstad in the ordinary case and by Kottwitz and Shelstad in the twisted case. The definition is abstract. For classical groups, we compute explicitely these factors

Calcul d'une valeur d'un facteur epsilon par une formule int\'egrale

Let d and m be two natural numbers of distinct parities. Let $\pi$ be an admissible irreducible tempered representation of GL(d,F), where F is a p-adic field. We assume that $\pi$ is self-dual. Then we can extend $\pi$ as a representation $\tilde{\pi}$ of a non-connected group $GL(d,F)\rtimes \{1,\theta\}$. Let $\rho$ be a representation of GL(m,F). We assume that it has similar properties as $\pi$. Jacquet, Piatetski-Shapiro and Shalika have defined the factor $\epsilon(s,\pi\times\rho,\psi)$. We prove that we can compute $\epsilon(1/2,\pi\times\rho,\psi)$ by an integral formula where occur the characters of $\tilde{\pi}$ and $\tilde{\rho}$. It's similar to the formula which, for special orthogonal groups, computes the multiplicities appearing in the local Gross-Prasad conjecture

Une variante d'un r\'esultat de Aizenbud, Gourevitch, Rallis et Schiffmann

Aizenbud, Gourevitch, Rallis and Schiffmann proves results of multicity one in different cases, in particular for orthogonal groups. Using the same method, we prove the same result for special orthogonal groups