Related papers: Local-global compatibility for l=p, I

We prove the equivalence of two conjectural constructions of unramified cuspidal automorphic functions on the adelic group GL_n(A) associated to an irreducible l-adic local system of rank n on an algebraic curve X over a finite field. The…

We prove a non-minimal modularity lifting theorem for ordinary Galois representations over imaginary quadratic fields, conditional on a local-global compatibility conjecture for ordinary torsion classes.

In the basic general frame of the Langlands global program, a local p-adic elliptic semimodule corresponding to a local (left) cuspidal form is constructed from its global equivalent covered by p-th roots. In the same context, global and…

Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…

In the 80's Aschbacher classified the maximal subgroups of almost all of the finite almost simple classical groups. Essentially, this classification divide these subgroups into two types. The first of these consist roughly of subgroups that…

Let $F$ be a non-archimedean local field of odd characteristic $p > 0$. In this paper, we consider local exterior square $L$-functions $L(s,\pi,\wedge^2)$, Bump-Friedberg $L$-functions $L(s,\pi,BF)$, and Asai $L$-functions $L(s,\pi,As)$ of…

We propose a p-adic Langlands correspondence in families.

We prove the existence of non-classical $p$-adic automorphic eigenforms associated to a classical system of eigenvalues on definite unitary groups in $3$ variables. These eigenforms are associated to Galois representations which are…

We prove the indecomposability of Galois representation restricted to the p-decomposition group attached to a non CM nearly p-ordinary weight two Hilbert modular form under mild conditions.

Let \Pi\ be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual \Pi\ with…

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system $E$ of…

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,…

Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of Sp(4). We give an explicit expression for the cohomology of…

Let $\rho$ be the $p$-adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of $\mathrm{GL}_n$ of unitary type. Under very mild hypotheses on $\rho$, we prove the vanishing of the (Bloch--Kato)…

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…

It is proved that certain types of modular cusp forms generate irreducible automorphic representation of the underlying algebraic group. Analogous archimedean and non-archimedean local statements are also given.

In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity…

Let $K$ be a $p$-adic local field. In this work we study a special kind of $p$-adic Galois representations of it. These representations are similar to the Galois representations occurred in the exceptional zero conjecture for modular forms.…

Let $K$ be a number field and let $E/K$ be an elliptic curve whose mod $\ell$ Galois representation locally has image contained in a group $G$, up to conjugacy. We classify the possible images for the global Galois representation in the…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$ with Galois automorphism $\sigma$, and let $R$ be an algebraically closed field of characteristic $\ell\notin\{0,p\}$. We…