Related papers: Computation of a universal deformation ring

Let R^univ be the universal deformation ring of a residual representation of a local Galois group. Kisin showed that many loci in MaxSpec(R^univ[1/p]) of interest are Zariski closed, and gave a way to study the generic fiber of the…

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…

Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$…

In this paper, we show the existence of a non-solvable Galois extension of $\Q$ which is unramified outside 2. The extension $K$ we construct has degree $2251731094732800=2^{19}(3\cdot 5\cdot 17\cdot 257)^2$ and has root discriminant…

We consider a mod 7 Galois representation attached to a genus 2 Siegel cuspforms of level 1 and weight 28 and using some of its Fourier coefficients and eigenvalues computed by N. Skoruppa and the classification of maximal subgroups of…

We prove two "large images" results for the Galois representations attached to a degree $d$ Q-curve $E$ over a quadratic field $K$: if $K$ is arbitrary, we prove maximality of the image for every prime $p >13$ not dividing $d$, provided…

In this paper we present a description of the Galois representation attached to an elliptic curve defined over a $2$-adic field $K$, in the case where the image of inertia is non-abelian. There are two possibilities for the image of…

Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the…

A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…

For an integer $m\geq 2$, we aim to investigate the realizability of types of metacyclic-nonmodular groups, whose abelianization is $\mathbb{Z}/2 \mathbb{Z}\times\mathbb{Z}/2^m \mathbb{Z}$, as the Galois group of the maximal unramified…

Let $K/\mathbb{Q}$ be a finitely generated field of characteristic zero and $X/K$ a smooth projective variety. Fix $q\in\mathbb{N}$. For every prime number $\ell$ let $\rho_\ell$ be the representation of $\mathrm{Gal}(K)$ on the \'etale…

Let $O$ be a nilpotent orbit of a complex semisimple Lie algebra $\mathfrak{g}$ and let $\pi: X \to \bar{O}$ be the finite covering associated with the universal covering of $O$. In the previous article we have explicitly constructed a…

As a sequel to our proof of the analog of Serre's conjecture for function fields in Part I of this work, we study in this paper the deformation rings of $n$-dimensional mod $\ell$ representations $\rho$ of the arithmetic fundamental group…

We consider the distribution of the Galois groups $\operatorname{Gal}(K^{\operatorname{un}}/K)$ of maximal unramified extensions as $K$ ranges over $\Gamma$-extensions of $\mathbb{Q}$ or $\mathbb{F}_q(t)$. We prove two properties of…

We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2)…

In this paper, we compare a certain field arising from the pro-$p$ outer Galois representation associated to a once-punctured CM elliptic curve over an imaginary quadratic field $K$ with the maximal pro-$p$ Galois extension of the mod-$p$…

We make a preliminary algebraic study of supersymmetric deformations of N=1 Yang-Mills theory in dimension ten with an arbitrary gauge group. This is done in a context of Lie algebra deformation theory. The tangent space to the space of…

In this article, we use deformation theory of Galois representations valued in the symplectic group of degree four to prove a freeness result for the cohomology of certain quaternionic unitary Shimura variety over the universal deformation…