Related papers: Stabilisation et germes pour $SL(2)$ en toutes car…

It is the second article of a series whose final goal is the stabilization of the twisted trace formula. Over a non archimedean field, we define (after Arthur) wheighted orbital integrals and their stable and endoscopic versions. We state…

Let $F$ be a local field of characteristic $p$ and $G$ be a connected reductive group over $F$. Recall that Shalika's germ expansion of orbital integrals of regular semi-simple elements near the identity, when it exists, is a sum indexed by…

We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about…

Let F be a number field and $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of Weil of $\mathrm{Sp}(2n, \mathbb{A}_F)$. We stabilize the elliptic semi-simple terms of the genuine part of trace formula for…

It is one of a series of articles whose goal is to stabilize the twisted trace formula. In two previous papers, we have considered the stabilization of weighted orbital integrals over a non-archimedean local field. Here we consider the…

In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur…

We begin the proof of the stabilization of the twisted trace formula. Here we prove that almost all "coefficients" appearing in this formula are equal to their endoscopic counterpart. It is the generalization to the twisted case of the…

The trace formula constitutes a fundamental tool in the Langlands program. In general, Arthur introduced a truncation operator to render both the geometric and spectral sides of the formula convergent. This paper focuses on the case of…

We prove a geometric local constancy theorem for affine Springer fibers in families of close local fields. Consequently, stable orbital integrals are locally constant in these families, and both the base change fundamental lemma and the…

The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp$(4)$ with automorphic representations of GL$(4)$ which are distinguished with respect to a…

In the preceeding article, we have generalized to the twisted case the proposition 3.1 of the third Arthur's article on the stabilization of the trace formula. The base-field was p-adic. Here, we prove the same result over the real…

Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for $\mathrm{Sym}^{n}$ lifting from $\mathrm{GL}_{2}$ to $\mathrm{GL}_{n+1}$ over any local fields $F$ of characteristic zero with residue…

Let $\pi$ be an irreducible admissible (complex) representation of $GL(2)$ over a non-archimedean characteristic zero local field with odd residual characteristic. In this paper we prove the equality between the local symmetric square…

We construct stable geometric and spectral transfer factors for a general reductive group and develop some of their basic properties, assuming the refined local Langlands correspondence. Using our definition of stable geometric transfer…

We express the discrete noncuspidal terms in the spectral side of the trace formula for GL(2) in terms of orbital integrals, obtaining a geometric expansion for the cuspidal part of the trace formula. Assuming the Ramanujan conjecture for…

In this work we prove that the local $\gamma$-factor arising from the doubling integrals for split general spin groups is stable. This deep property of the $\gamma$-factor constitutes an important ingredient in the application of the…

Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension…

We rewrite Arthur's asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients…

Let $F$ be a non-archimedean local field of characteristic not equal to $2$ and let $E/F$ be a quadratic algebra. We prove the stability of local factors attached to (complex) irreducible admissible representations of $GL(2,E)$ via the…

We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…