Related papers: Local Langlands correspondence and ramification fo…

We study the local zeta functions of an algebraic group $\mathcal{G}$ defined over $\mathfrak{K}$ together with a faithful $\mathfrak{K}$-rational representation $\rho$ for a finite extension $\mathfrak{K}$ of $\mathbb{Q}$. These are given…

Let $G$ be a reductive algebraic group defined over a non-Archimedean local field $F$ of residue characteristic $p$. Let $\sigma$ be an automorphism of $G$ of order $\ell$ -- a prime number -- with $\ell\neq p$. Let $\Pi$ be a finite length…

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

This article deals with the tamely ramified geometric Langlands correspondence for GL_2 on $\mathbf{P}_{\mathbf{F}_q}^1$, where $q$ is a prime power, with tame ramification at four distinct points $D = \{\infty, 0,1, t\} \subset…

We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has…

We prove a result which provides a link between the decomposition of parabolically induced representations and the Bushnell--Kutzko theory of typical representations. As an application, we show that there exists a well-defined inertial…

We consider the category of depth $0$ representations of a $p$-adic quasi-split reductive group with coefficients in $\overline{\mathbb{Z}}[\frac{1}{p}]$. We prove that the blocks of this category are in natural bijection with the connected…

We show that when $p$ is an odd prime, $K$ is an unramified finite extension of $\mathbb Q_p$ and $G$ is a pure inner form of an unramified special orthogonal group or unitary group over $K$, the Fargues-Scholze local Langlands…

In our previous paper [math.NT/0408050], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces $X$ attached to real orthogonal groups of type…

Let $X=G/H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$-invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly on $X$ and $\Gamma$ a torsion-free discrete subgroup of $L$.…

We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\mathbb{Z}[\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\mathrm{G}$ (where $q$ is the cardinality of the…

We provide an explicit construction of the local Langlands correspondence for general tamely-ramified reductive p-adic groups and a class of wildly ramified Langlands parameters. Furthermore, we verify that our construction satisfies the…

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are…

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification…

Let $F$ be a non-archimedean local field of odd residual characteristic. We compute the Jordan set of a simple cuspidal representation of a symplectic group over $F$, using explicit computations of generators of the Hecke algebras of covers…

Let $G$ be a simple group over a global function field $K$, and let $\pi$ be a cuspidal automorphic representation of $G$. Suppose $K$ has two places $u$ and $v$ (satisfying a mild restriction on the residue field cardinality), at which the…

Based upon the general theory, developed by the author, on the parametrization of the irreducible representations of the hyper special compact groups corresponding to the regular adjoint orbit, supercuspidal representations of $SL_n(F)$ are…

For a cardinal $\kappa$, denote by $\mathbf{H}^\kappa$ the algebraic real hyperbolic space of dimension $\kappa$. For a topological group $\Gamma$, we study the set of continuous representations $\Gamma \to…

We provide a definition for an extended system of $\gamma$-factors for products of generic representations $\tau$ and $\pi$ of split classical groups or general linear groups over a non-archimedean local field of characteristic $p$. We…

In \cite{lafforgue2012chtoucas}, Vicent Lafforgue attaches a semisimple Langlands parameter (or, what amounts to the same thing, a $\hat{G}$-pseudocharacter) to every cuspidal automorphic representation of a reductive group $G$ over the…