Related papers: Rigid G2-Representations and motives of Type G2

Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension…

The paper is concerned with the following version of Hilbert's irreducibility theorem: if $\pi: X \to Y$ is a Galois $G$-covering of varieties over a number field $k$ and $H \subset G$ is a subgroup, then for all sufficiently large and…

Let $G$ and $N$ be finite groups of order $2n$ where $n$ is odd. We say the pair $(G,N)$ is Hopf-Galois realizable if $G$ is a regular subgroup of $\h(N)=N\rtimes\au(N)$. In this article we give necessary conditions on $G$ (similarly $N$)…

Let $p$ be a prime number and $F$ a local field with residual characteristic $p$. In this article, to an irreducible smooth representation of $GL_2(F)$ over $\bar{\mathbf{F}}_p$ with central character, we associate canonically a diagram…

This article advances the results of Duke on the average surjectivity of Galois representations for elliptic curves to the context of Drinfeld modules over function fields. Let $F$ be the rational function field over a finite field. I…

In this article, we prove the existence of rigid analytic families of $G$-stable lattices with locally constant reductions inside families of representations of a topologically compact group $G$, extending a result of Hellman obtained in…

We classify principal $2$-blocks of finite groups $G$ with Sylow $2$-subgroups isomorphic to a wreathed $2$-group $C_{2^n}\wr C_2$ with $n\geq 2$ up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain…

Let $\rho\colon G\to \mathrm{GL}_2(K)$ be a continuous representation of a compact group $G$ over a complete discretely valued field $K$, with ring of integers $\mathcal O$ and uniformiser $\pi$. We prove that $\operatorname{tr}\rho$ is…

For a rational prime $p \geq 3$ and an integer $n \geq 2$, we study the modularity of continuous 2-dimensional mod $p^n$ Galois representations of $\Gal(\bar{\Q}/\Q)$ whose residual representations are odd and absolutely irreducible. Under…

The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

We give an effective version of a result reported by Serre asserting that the images of the Galois representations attached to an abelian surface with $\End(A)= \mathbb{Z}$ are as large as possible for almost every prime. Our algorithm…

Let $G$ be the simple algebraic group $SL_2$ defined over an algebraically closed field $K$ of characteristic $p>0$. In this paper, we find the second cohomology of all irreducible representations of $G$

In this letter we show that for certain infinite families of modular forms of growing level it is possible to have a control result for the exceptional primes of the attached Galois representations. As an application, a uniform version of a…

It is proved that the profinite completion of the mapping class group Mod (g,n) of a surface of genus g with n boundary components is isomorphic to such of the arithmetic group GL(6g-6+2n, Z). We establish a relation between the normal…

We review some results and techniques from our papers devoted to the computation of motivic classes of stacks of parabolic Higgs budles and bundles with connections on a curve. In the last section we present some directions for future work,…

Given a finite group G, we develop a theory of G-equivariant noncommutative motives. This theory provides a well-adapted framework for the study of G-schemes, Picard groups of schemes, G-algebras, 2-cocycles, equivariant algebraic K-theory,…

Let $L/F$ be a finite Galois extension of number fields with an arbitrary Galois group $G$. We give an explicit description of the kernel of the natural map on motivic tame kernels $H^2_{\mathcal{M}}(o_L, {\bf Z}(i))_{G} {\rightarrow}…

Let $\pi_1$ and $\pi_2$ be absolutely irreducible smooth representations of $G=GL_2(Q_p)$ with a central character, defined over a finite field of characteristic $p$. We show that if there exists a non-split extension between $\pi_1$ and…

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a…

We prove modularity of some two dimensional, 2-adic Galois representations over totally real fields that are nearly ordinary and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families,…