Related papers: On the Local Converse Theorem for p-adic GLn

Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of…

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this paper, we…

We present a collection of results on a conjecture of Jannsen about the $p$-adic realizations associated to Hecke characters over an imaginary quadratic field $K$ of class number 1. The conjecture is easy to check for Galois groups purely…

In this paper, we give a simple and short proof of the uniqueness of generic representations in an $L$-packet for a quasi-split connected classical group over a non-archimedean local field.

In this paper we will algorithmically prove the local and global epsilon constant conjectures for all fields of absolute degree lower or equal to 15. To this end we will present an efficient algorithm for the computation of local…

Let G be a quasi-split p-adic group. Under the assumption that the local coefficients $C_{\psi}$ defined with respect to $\psi $-generic tempered representations of standard Levi subgroups of G are regular in the negative Weyl chamber, we…

In a recent paper, Colliot-Th\'el\`ene, Parimala and Suresh conjectured that a local-global principle holds for projective homogeneous spaces of connected linear algebraic groups over function fields of p-adic curves. In this paper, we show…

The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…

Let K be a complete discretely valued field with residue field k and F be a function field of a curve over K. Let L/F be a Galois extension of degree n. If n is coprime to char(k), then under some assumptions on k(e.g. k is algebraically…

We show that for a monic polynomial $f(x)$ over a number field $K$ containing a global permutation polynomial of degree $>1$ as its composition factor, the Newton Polygon of $f\mod\mathfrak p$ does not converge for $\mathfrak p$ passing…

In this paper a proof of Conjecture 9.12 of Braverman and Kazhdan in their article "gamma-functions of representations and lifting" on the acyclicity of their l-adic gamma-sheaves over certain affine spaces is given for GL(n).

We study in detail certain natural continuous representations of G = GL(n,K) in locally convex vector spaces over a locally compact, non-archimedean field K of characteristic zero. We construct boundary value maps, or integral transforms,…

We prove the local Langlands correspondence for GSp_4(F), where F is a non-archimedean local field of positive characteristic with residue characteristic > 2.

Let $F$ be a nonarchimedean local field of characteristic zero and odd residual characteristic. Let $X$ be the $p$-adic symmetric space $X = H \backslash G$, where $G = \mathbf{GL}_{2n}(F)$ and $H = \mathbf{GL}_n(F) \times…

The Conifold Gap Conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes $G$-function. In this paper, I…

We compare different local-global principles for torsors under a reductive group G defined over a semiglobal field F. In particular if the F-group G s a retract rational F-variety, we prove that the local global principle holds for the…

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension $\G$ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we…

In this paper we formulate a conjecture on the relationship between the equivariant \epsilon-constants (associated to a local p-adic representation V and a finite extension of local fields L/K) and local Galois cohomology groups of a Galois…

The main aim of this paper is to present the ideas which lead first to the solution of the unitarizability problem for $\GL(n)$ over nonarchimedean local fields and to the recognition that the same result holds over archimedean local…

Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon…