Related papers: Mod p Base Change transfer for GL(2)

La correspondance de Langlands locale p-adique pour GL_2(Q_p) est une bijection entre certaines representations de dimension 2 de Gal(Q_p^bar/Q_p) et certaines representations de GL_2(Q_p). Cette bijection peut en fait etre construite en…

Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida regarding the {\it congruence number}…

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level…

We give a geometric interpretation of the base change homomorphism between the Hecke algebra of GL(n) for an unramified extension of local fields of positive characteristic. For this, we use some results of Ginzburg, Mirkovic and Vilonen…

Let F be a p-adic field with residue class field k. We investigate the structure of certain mod p universal modules for GL(3,F) over the corresponding Hecke algebras. To this end, we first study the structure of some mod p universal modules…

A fundamental question, first raised by Langlands, is to know whether the Rankin-Selberg product of two (not necessarily holomorphic) cusp forms f and g is modular, i.e., if there exists an automorphic form f box g on GL(4)/Q whose standard…

In this paper, we investigate the "angular changes" behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts…

In the Cohen-Glashow Very Special Relativity we exhibit possible modifications to the Maxwell theory and to the quantum electrodynamics Lagrangian in some generality, and discuss characteristic features depending on the modifications.…

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.

Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly…

We fix a prime number $p$ and $\K$ a number field, we denote by $M$ the maximal abelian $p$-extension of $\Ko$ unramified outside $p$. The aim of this paper is to study the $\Z_p$-module $\gal(M/\Ko)$ and to give a method to effectively…

On d\'emontre une conjecture due \'a N. Kuhn concernant la cohomologie singuli\'ere \'a coefficients mod p des espaces, comme module instable sur l'alg\'ebre de Steenrod. Notre d\'emonstration de ce r\'esultat, d\'ej\'a connu en…

The use of overconvergent cohomology in constructing $p$-adic $L$-functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been established in a number of settings. The method is compatible…

Let $f$ be a newform of weight $2$ on $\Gamma_0(N)$ with Fourier $q$-expansion $f(q)=q+\sum_{n\geq 2} a_n q^n$, where $\Gamma_0(N)$ denotes the group of invertible matrices with integer coefficients, upper triangular mod $N$. Let $p$ be a…

We establish the functorial transfer of generic, automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields, completing an earlier project. Our results are definitive and, in…

Statistics transmutations to composite fermions in fractional-quantum-Hall-effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground-state energy shows that the transmutations are not…

Let $F$ be a field of characteristic $p$ and let $E/F$ be a purely inseparable field extension. We study the group $H_p^{n+1}(F)$ of classes of differential forms under the restriction map $H_p^{n+1}(F)\to H_p^{n+1}(E)$ and give a system of…

Let $p>2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a mod $p$ Galois representation to arise from a mod $p$ Hilbert modular form of parallel weight one, by proving a…

These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory…

We compute the non-Eisenstein systems of Hecke eigenvalues contributing to the $p$-arithmetic homology of irreducible smooth mod $p$ representations $\pi$ of $\mathrm{GL}_2(\mathbb{Q}_p)$ and to the cohomology of their duals. We show that…