Related papers: Eigenvarieties over CM fields and trianguline repr…

In this paper, we study the Galois representations attached to products of Drinfeld modules. As an analogue of Serre's classical result on the images of Galois representations associated with products of elliptic curves, we prove that for…

The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce…

The aim of this article is to study rank-one Eisenstein cohomology for the group GL(N)/F, where F is a totally real field extension of Q. This is then used to prove rationality results for ratios of successive critical values for…

This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the…

Let $S$ be a Shimura variety with reflex field $E$. We prove that the action of $\operatorname{Gal}(\overline{\mathbb{Q}}/E)$ on $S$ maps special points to special points and special subvarieties to special subvarieties. Furthermore, the…

Generically, one can attach to a Q-curve C octahedral representations Gal(Qbar/Q) --> GL(2,Fbar_3) coming from the Galois action on the 3-torsion of those abelian varieties of GL_2-type whose building block is C. When C is defined over a…

We prove a potentially automorphy theorem for suitable Galois representations $\Gamma_{F^+} \to \mathrm{GSpin}_{2n+1}(\overline{\mathbb{F}}_p)$ and $\Gamma_{F^+} \to \mathrm{GSpin}_{2n+1}(\overline{\mathbb{Q}}_p)$, where $\Gamma_{F^+}$ is…

Let $m$ be an integer greater than three and $\ell$ be an odd prime. In this paper, we prove that at least one of the following groups: $\mbox{P}\Omega^\pm_{2m}(\mathbb{F}_{\ell^s})$, $\mbox{PSO}^\pm_{2m}(\mathbb{F}_{\ell^s})$,…

We study the image of the $\ell$-adic Galois representations associated to the four vector valued Siegel modular forms appearing in the work of Chenevier and Lannes. These representations are symplectic of dimension $4$. Following a method…

We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GL_n(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the…

Let $K$ be a field, $L$ a finite Galois extension of $K$, and $X$ an abelian variety defined over $L$. If $X$ is isogenous over $L$ to an abelian variety defined over $K$, then the $\ell$-adic Galois representations associated to $X$ extend…

In 1994, van Geemen and Top constructed a non-selfdual motive of rank three over $\mathbb{Q}$ conjecturally associated with a cuspidal non-selfdual automorphic representation of $\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$ of level…

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow…

We prove a version of the weight part of Serre's conjecture for mod $p$ Galois representations attached to automorphic forms on rank 2 unitary groups which are non-split at $p$. More precisely, let $F/F^+$ denote a CM extension of a totally…

We discuss the following two problems: 1) The properties of the multiple zeta-values and their generalizations, multiple polylogarithms at N-th roots of unity; 2) The action of the absolute Galois group on the pro-l-completion of the…

We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and…

To each Drinfeld module over a finitely generated field with generic characteristic, one can associate a Galois representation arising from the Galois action on its torsion points. Recent work of Pink and R\"utsche has described the image…

We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation variety and associated tangent spaces.

We pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and discuss some supporting evidence on the conjectures. Especially, we show that the conjectures hold if a Galois descent of a $K_3$-group is satisfied.

Given a compatible system of n-dimension l-adic Galois representations arising from \'etale cohomology of any complete, non-singular variety, we prove that for sufficiently large prime l, type A Galois image (in the Cartan-Killing…