Related papers: On close fields and the local Langlands correspond…

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

In 1967, Langlands conjectured a natural correspondence between automorphic representations and Galois representations, over number fields as well as over function fields. In 1983, Drinfeld discovered a geometric analog of the Langlands…

We construct Igusa stacks for all Shimura varieties of abelian type and derive consequences for the cohomology of these Shimura varieties. As an application, we prove that the Fargues--Scholze local Langlands correspondence agrees with the…

In the present article we define coverings of affine Deligne-Lusztig varieties attached to a connected reductive group over a local field of characteristic $p > 0$. In the case of $\GL_2$, the unramified part of the local Langlands…

Refined forms of the local Langlands correspondence seek to relate representations of reductive groups over local fields with sheaves on stacks of Langlands parameters. But what kind of sheaves? Conjectures in the spirit of Kazhdan-Lusztig…

Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of…

Let $F$ be a non-archimedean local field of characteristic not equal to 2. In this paper, we prove the local converse theorem for quasi-split $\O_{2n}(F)$ and $\SO_{2n}(F)$, via the description of the local theta correspondence between…

Let $F$ be a non archimedean local field of residual characteristic $p$ and $\ell$ a prime number different from $p$. Let $\mathrm{V}$ denote Vign\'eras' $\ell$-modular local Langlands correspondence between irreducible $\ell$-modular…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

Let $F$ be a non-archimedean locally compact field. We study a class of Langlands-Shahidi pairs $({\bf H},{\bf L})$, consisting of a quasi-split connected reductive group $\bf H$ over $F$ and a Levi subgroup $\bf L$ which is closely related…

Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical…

This paper proves the local Langlands conjecture for the non quasi-split inner form Sp(1,1) of Sp(4) over a p-adic field of characteristic 0, by studying the restriction of representations from the non quasi-split inner form GSp(1,1) of…

We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.

We show that the Fargues--Fontaine curve associated to an algebraically closed field of characteristic p is geometrically simply connected; that is, its base extension from Q_p to any complete algebraically closed overfield admits no…

We generalize the work of M. Harris and R. Taylor on the local Langlands correspondence for the linear group over $\mathbb{Q}_p$. We prove some cases of the Kottwitz conjectures for the supercuspidal part of the compactly supported…

Let $\ell$ and $p$ be distinct primes, $n$ a positive integer, $F_\ell$ an $\ell$-adic local field of characteristic $0,$ and let $W(k)$ denote the ring of Witt vectors over an algebraically closed field of characteristic $p$. Work of…

The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…

We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of…

Using theta correspondence, we obtain a classification of irreducible representations of an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from the local Langlands correspondence for symplectic…

Given a quasi-split connected reductive $\mathbb{R}$-group $G$ and a finite group $A$ acting on $G$ by $\mathbb{R}$-automorphisms that preserve an $\mathbb{R}$-pinning, we construct for each discrete $L$-parameter for $G$ a corresponding…