Related papers: A note about rational representations of different…

In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…

It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group representations, we give a unified approach to such results.

We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…

In Picard-Vessiot theory, the Galois theory for linear differential equations, the Picard-Vessiot ring plays an important role, since it is the Picard-Vessiot ring which is a torsor (principal homogeneous space) for the Galois group…

Let k be a differential field and C its subfield of constants. In general a differential extension K of k add some new constants to C, and it is difficult to prove that C stay unchangeable under the extension K; This situation is provided…

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…

We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending…

We show that finite Galois extensions with cyclic Galois group are radical.

We give a description of the Picard group of a reductive group over a number field as an abelianized Galois cohomology group. It gives another approach of a result due to Labesse.

We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois…

For every nonconstant rational function $\phi\in\mathbb{Q}(x)$, the Galois groups of the dynatomic polynomials of $\phi$ encode various properties of $\phi$ that are of interest in the subject of arithmetic dynamics. We study here the…

We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation of the form $…

We give an algebraic characterization of Picard-Fuchs operators attached to families of Calabi-Yau manifolds with a point of maximally unipotent monodromy and discuss possibilities for their differential Galois groups.

We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of…

We study the differential Galois theory of difference equations under weaker hypothesis on the field of constants of the automorphism. This framework yields a new approach to results by C.Hardouin and M.Singer, which answers possitively a…

Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. The differential representation…

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,…

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.

We give simple necessary and sufficient conditions for the $\frac{\partial}{\partial t}$-transcendence of the solutions to a parameterized second order linear differential equation of the form \frac{\partial^2 Y}{\partial x^2} - p…