Related papers: Endoscopic decomposition of elliptic Fargues-Schol…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

We establish the endoscopic character identity for bounded $A$-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the…

Let $F$ be a non-archimedean local field. Let $\overline{F}$ be an algebraic closure of $F$. Let $G$ be a connected reductive group over $F$. Let $\varphi$ be an elliptic $L$-parameter. For every irreducible representation $\pi$ of $G(F)$…

Let $G \subseteq \tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der} = \tilde{G}_{der}$. Although the existence of L-packets is still conjectural in general, it is believed that the…

We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets using endoscopy.

We prove the conjectural endoscopic transfer of L-packets for the local Langlands correspondence for pure inner forms of unramified p-adic groups and depth-zero parameters established by DeBacker and Reeder. More precisely, we show that…

In this paper we gives the Langlands parameters of Langlands' packets of discrete series using the twisted endoscopy as explained by Arthur; this holds for orthogonal, symplectic, unitary and G-Spin groups and gives the most simple proof…

Given a number field we construct a canonical Galois gerbe over it and show that its cohomology provides a bridge between the refined local endoscopy introduced in arXiv:1304.3292 and classical global endoscopy. As particular applications,…

Let $G$ be a connected reductive group over a field $F=\mathbb{F}_q((t))$ splitting over $\overline{\mathbb{F}}_q((t))$. Following [KV,DR], a tamely unramified Langlands parameter $\lambda:W_F\to{}^L G(\overline{\mathbb{Q}}_{\ell})$ in…

Let $F$ be a global field, and $G$ a connected reductive group defined over $F$. We prove that two endoscopic data of $G$ which are equivalent almost everywhere, are equivalent. The result remains true for (non-twisted) endoscopy with…

This is the first of a series of papers devoted to the stabilization of the twisted trace formula. It is just an introduction. We present the local theory of twisted endoscopy, following the fundamental works of Kottwitz-Shelstad, Labesse…

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series…

Genestier--Lafforgue and Fargues--Scholze have constructed a semisimple local Langlands paramterization for reductive groups over equicharacteristic local fields. Assuming a version of the stable twisted trace formula for function fields,…

We prove the existence of generalized characteristics for weak, not necessarily entropic, solutions of Burgers' equation \[ \partial_t u +\partial_x \frac{u^2}{2} =0, \] whose entropy productions are signed measures. Such solutions arise in…

We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of…

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 p-adic field and let G be a connected reductive group defined over F. We assume p is big. Denote g the Lie algebra of G. We normalize suitably a Fourier-transform on the space of smooth functions with compact support on g(F),…

Let $P$ be the Gelfand--Tsetlin polytope defined by the skew shape $\lambda/\mu$ and weight $w$. In the case corresponding to a standard Young tableau, we completely characterize for which shapes $\lambda/\mu$ the polytope $P$ is integral.…

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…