Related papers: The local Langlands correspondence for GL(n) over …

We give a parametrization of the simple Bernstein components of inner forms of a general linear group over a local field by invariants constructed from type theory, and explicitly describe its behaviour under the Jacquet-Langlands…

We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect…

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…

Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.

This paper surveys what is known about (conjectural) $p$-adic and $p$-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary group…

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.

Let K/F be a tamely ramified quadratic extension of non-archimedean locally compact fields. Let GL_m (D) be an inner form of GL_n (F) and GLp(R) = (M_m (D) \otimes K)^{\times} . Then GLp(R) is an inner form of GL_n (K). In this work, we…

In this paper, we will calculate the number of Galois extensions of local fields with Galois group A_n and S_n.

We describe the de Rham complex of the \'etale coverings of Drinfeld's p-adic upper half-plane for GL_2(Q_p). Conjectured by Breuil and Strauch, this description gives a geometric realization of the p-adic local Langlands correspondence for…

Let $F$ be a non-Archimedean local field. Let $\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\textrm{GL}_n(F)$, and $\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional…

This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…

Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…

We generalise Coleman's construction of Hecke operators to define an action of GL_2(Q_l) on the space of finite slope overconvergent p-adic modular forms (l not equal p). In this way we associate to any C_p-valued point on the tame level N…

The goal of these notes is to give a self-contained account of the representation theory of $GL_2$ and $SL_2$ over a finite field, and to give some indication of how the theory works for $GL_n$ over a finite field.

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

This is a review of Parshin's higher local class field theory in characteristic p.

Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation $\pi$ for $\U(3)$, the $l$-adic Galois representation $\rho_l$ which is…

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…

The goal of this paper is to give an explicit description of the integrable structure of the Hitchin moduli spaces. This is done by introducing explicit parameterisations for the different strata of the Hitchin moduli spaces, and by…

We prove that V. Lafforgue's global Langlands correspondence is compatible with Fargues-Scholze's semisimplified local Langlands correspondence. As a consequence, we canonically lift Fargues-Scholze's construction to a non-semisimplified…