Related papers: l-Adic representations associated to modular forms…

Let $X$ be a normal algebraic variety over a finitely generated field $k$ of characteristic zero, and let $\ell$ be a prime. Say that a continuous $\ell$-adic representation $\rho$ of $\pi_1^{\text{\'et}}(X_{\bar k})$ is arithmetic if there…

Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ defined on $GL_n(\mathbb{A}_E)$ and $GL_m(\mathbb{A}_F)$, respectively, with $E$ and $F$ solvable algebraic number fields we deduce a prime number theorem for the…

We construct p-adic Asai L-functions for cuspidal automorphic representations of GL2 / F, where F is a real quadratic field in which p splits. Our method relies on higher Hida theory for Hilbert modular surfaces with Iwahori level at one…

Suppose $\rho_1, \rho_2$ are two $\ell$-adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations is connected and the representations are locally…

Given an abelian variety $A$ of dimension $g$ over a number field $K$, and a prime $\ell$, the $\ell^n$-torsion points of $A$ give rise to a representation $\rho_{A, \ell^n} : \gal(\bar{K} / K) \to \gl_{2g}(\zz/\ell^n\zz)$. In particular,…

It is proved that every two-dimensional residual Galois representation of the absolute Galois group of an arbitrary number field lifts to a characteristic zero $p$-adic representation, if local lifting problems at places above $p$ are…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$, and let $\sigma$ denote its non-trivial automorphism. Let $R$ be an algebraically closed field of characteristic different…

Given a self-dual cuspidal automorphic representation for GL(2) over a number field, we establish the existence of an infinite number of Hecke eigenvalues that are greater than an explicit positive constant, and an infinite number of Hecke…

We introduce a notion of inertial equivalence for integral $\ell$-adic representation of the Galois group of a global field. We show that the collection of continuous, semisimple, pure $\ell$-adic representations of the absolute Galois…

Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of…

The arithmetic of Hilbert modular forms has been extensively studied under the assumption that the forms concerned are "paritious" -- all the components of the weight are congruent modulo 2. In contrast, non-paritious Hilbert modular forms…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

In this paper we show that two dimensional (mod p) Galois representations satisfying mild hypotheses can be lifted to p-adic Galois representations ramified at infinitely many primes such that the characteristic polynomials of Frobenius at…

We consider the problem of recovering l-adic representations from a knowledge of the character values at the Frobenius elements associated to l-adic representations constructed algebraically out of the original representations. These…

We give a parametrization of the possible Serre invariants $(N,k,\nu)$ of modular mod $\ell$ Galois representations of the exceptional types $A_4$, $S_4$, $A_5$, in terms of local data attached to the fields cut out by the associated…

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $GL_n$…

We prove that for any m > 1 given any m-tuple of Hecke eigenforms $f_i$ of level 1 whose weights satisfy the usual regularity condition there is a self-dual cuspidal automorphic form $\pi$ of $\GL_{2^m}(\Q)$ corresponding to their tensor…

Let G be the group of rational points of a quasi-split p-adic special orthogonal, symplectic or unitary group for some odd prime number p. FollowingArthur and Mok, there are a positive integer N, a p-adic field E and a local functorial…

Let $\pi$ be a polarized, regular algebraic, cuspidal automorphic representation of $\operatorname{GL}_n(\mathbb{A}_F)$ where $F$ is totally real or imaginary CM, and let $(\rho_\lambda)_\lambda$ be its associated compatible system of…