Related papers: On a Theorem of N. Katz and Bases in Irreducible R…

Motivated by the work of Liu, we study certain canonical quotients of $G_{\emptyset}^T(K)$ -- the Galois group of the maximal unramified extension of a global field $K$ that is split completely at a finite nonempty set of places in $T$ --…

We disprove a strong form of the Regular Inverse Galois Problem: there exist finite groups $G$ which do not have a realization $F/\Qq(T)$ that induces all Galois extensions $L/\Qq(U)$ of group $G$ by specializing $T$ to $f(U) \in \Qq(U)$.…

A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…

Given a hilbertian field $k$ of characteristic zero and a finite Galois extension $E/k(T)$ with group $G$ such that $E/k$ is regular, we produce some specializations of $E/k(T)$ at points $t_0 \in \mathbb{P}^1(k)$ which have the same Galois…

We find the irreducible decomposition of the Weil representation of the unitary group $\mathrm{U}_{2n}(A)$, where $A$ is a ramified quadratic extension of a finite, commutative, local, principal ideal ring $R$ and the nilpotency degree of…

Let $(\mathbb{T}_f,\mathfrak{m}_f)$ denote the mod $p$ local Hecke algebra attached to a normalised Hecke eigenform $f$, which is a commutative algebra over some finite field $\mathbb{F}_q$ of characteristic $p$ and with residue field…

In this paper we show how to construct, for most p >= 5, two types of surjective representations \rho:G_Q=Gal(\bar{Q}/Q) -> GL_2(Z_p) that are ramified at an infinite number of primes. The image of inertia at almost all of these primes will…

In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the…

In this article, we prove that for a convergent sequence of residually absolutely irreducible representations of the absolute Galois group of a number field $F$ with coefficients in a domain finite over a power series ring over a $p$-adic…

In this paper, we investigate finite-dimensional irreducible representations of the quantum affine general linear superalgebra $\mathrm{U}_q\big(\widehat{\mathfrak{gl}}_{m|n,\mathbf{s}}\big)$ for arbitrary 01-sequences $\mathbf{s}$, using…

We prove the following theorem: Let $\bar\F_p$ be an algebraic closure of a finite field of characteristic $p$. Let $\rho$ be a continuous homomorphism from the absolute Galois group of $\Q$ to $\GL(3,\bar\F_p)$ which is isomorphic to a…

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 study the irreducible components of special loci of curves whose group of symmetries is given as certain group extension. We introduce some relative Hurwitz data, which we show by using mixed \'etale cohomology theory, identifies some…

We prove some cases of the Fontaine-Mazur conjecture for even Galois representations. In particular, we prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of $\Gal(\Qbar/\Q)$…

We study the ramification groups of finite Galois extensions $L/K$ of a complete discrete valuation field $K$ of equal characteristic $p>0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices…

We study the number of ramified prime numbers in finite Galois extensions of $\mathbb{Q}$ obtained by specializing a finite Galois extension of $\mathbb{Q}(T)$. Our main result is a central limit theorem for this number. We also give some…

In this paper, we used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. The structures of the representations over the general linear…

Let G be a finite group and V a finite-dimensional rational G-representation. We ask whether there exists a finite Galois extension L/K of number fields with Galois group G, an elliptic curve E/K, and a G-submodule of E(L) tensor Q…

We give model theoretic accounts and proofs of the existence and uniqueness of differential Galois extensions with no new constants, for logarithmic differential equations over a differential field K, when the field C of constants of K is…

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…