Related papers: p-adic Jacquet-Langlands correspondence and patchi…

We prove some qualitative results about the $p$-adic Jacquet--Langlands correspondence defined by Scholze, in the $GL(2,Q_p)$, residually reducible case, by using a vanishing theorem proved by Judith Ludwig. In particular, we show that in…

Let $F$ be a non-archimedean local field. For any irreducible representation $\pi$ of an inner form $G'=\mathrm{GL}_{m}(D)$ of $G=\mathrm{GL}_{N}(F)$, there exists an irredubile representation of a maximal compact open subgroup in $G'$…

We prove that the global Jacquet--Langlands correspondence ${\rm JL}$ for ${\rm GL}(2)$ can be realized via tensor products over Hecke algebras. Let $G$ be a non-split inner form of ${\rm GL}(2)$ over a number field. Using the similitude…

In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them…

This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.

After observing that some constructions and results in the $p$-adic Langlands programme are somehow independent from $p$, we formulate the hypothesis that this astonishing uniformity could be explained by a 1-adic Langlands correspondence.

Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use…

We establish an explicit correspondence of certain Arthur packets between real unitary groups and $p$-adic symplectic or orthogonal groups. This allows one to compute Arthur packets of real unitary groups by translating results from the…

This is the second article in a two-part series presenting a new proof comparing the non-invariant trace formula for a general linear group with that of one of its inner forms. In this article, we focus on the spectral side of the trace…

We show how the modular representation theory of inner forms of general linear groups over a non-Archimedean local field can be brought to bear on the complex theory in a remarkable way. Let F be a non-Archimedean locally compact field of…

We use results by Chenevier to interpolate the classical Jacquet-Langlands correspondence for Hilbert modular forms, which gives us an extension of Chenevier's results to totally real fields. From this we obtain an isomorphisms between…

La correspondance de Langlands locale p-adique pour GL_2(Q_p) est une bijection entre certaines representations de dimension 2 de Gal(Q_p^bar/Q_p) et certaines representations de GL_2(Q_p). Cette bijection peut en fait etre construite en…

In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we…

In this paper, we prove that, if Deligne's "petites camarades conjecture" holds, then a Langlands type correspondence holds also for $p$-adic coefficients on a smooth curve over a finite field. We also prove that any overconvergent…

We develop a new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0. This first article is devoted…

We show that, over a nonarchimedean local field, the rigid refined local Langlands correspondence and associated endoscopic character identities for connected reductive $G$ follow if one only has them for all such $G$ with connected center.…

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are…

We prove the recent conjectures of Adams-Vogan and D. Prasad on the behavior of the local Langlands correspondence with respect to taking the contragredient of a representation. The proof holds for tempered representations of quasi-split…

We prove that the Jacquet-Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz's conjecture for Shimura varieties attached to unitary similitude…

We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a…