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

Extending results of Kazhdan to the relative case, we relate harmonic analysis over some spherical spaces G(F)/H(F), where F is a field of positive characteristic, to harmonic analysis over the spherical spaces G(E)/H(E), where E is a…

Let $\rho_\ell$ be a semisimple $\ell$-adic representation of a number field $K$ that is unramified almost everywhere. We introduce a new notion called weak abelian direct summands of $\rho_\ell$ and completely characterize them, for…

Let $G$ be a split connected reductive group defined over $\mathbb{Z}$. Let $F$ be a locally compact non-Archimedean field with residue characteristic $p$. For a locally compact non-Archimedean field $F'$ that is sufficiently close to $F$,…

We initiate the study of affine Deligne-Lusztig varieties with arbitrarily deep level structure for general reductive groups over local fields. We prove that for GLn and its inner forms, Lusztig's semi-infinite Deligne-Lusztig construction…

Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative…

We study the cohomology of various local Shimura varieties for $GL_n$. This provides an explicit description of the spectral action constructed by Fargues-Scholze in certain cases and allows us to prove some strongly generic part of the…

This paper refers to Langlands' big set of notes [L] devoted to the question if the (normalized) local Hecke-Tate root number $\Delta=\Delta(E,\chi)$, where $E$ is a finite separable extension of a fixed non-archimedean local field $F$, and…

We construct analogues of the Hecke operators for the moduli space of G-bundles on a curve X over a local field F with parabolic structures at finitely many points. We conjecture that they define commuting compact normal operators on the…

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…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

Let F be a non-Archimedean local field and let E be an unramified extension of F of degree n>1. To each sufficiently generic multiplicative character of E (the details are explained in the body of the paper) one can associate an irreducible…

We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic…

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\rm GL}_n, {\rm GL}_m)$ over a non-Archimedean locally compact field $F$. The proof consists in combining a study on Kudla's…

Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is…

We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their local Floer homology. In some cases, one may think of such intersections as modeled on…

Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for tame $G$-local systems over $X$ and logarithmic…

We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link…

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 exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field $\mathbb K$ of characteristic $\neq 2$ from scratch. We show that the formal model…

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…