Related papers: Tannakian Fundamental Groups Associated to Galois …

We prove that the fundamental group functor from categorical Galois theory may be computed as a Kan extension.

We prove that several properties of absolute Galois groups are preserved under a profinite completion.

The purpose of this paper is to constructively develop a Galois theory on irreducible shifts of finite type (SFTs) and to analyze the automorphism groups of SFTs using this framework. Let $X$ and $Y$ be irreducible SFTs. We demonstrate that…

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois…

We present a shortcut to the familiar characterizations of finite Galois extensions, based on an idea from an earlier Monthly note by Sonn and Zassenhaus.

This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic…

We show that for a complex abelian variety X a certain Tannaka group G(X) attached to X is a pro-reductive group whose group of connected components is abelian, and hence isomorphic to the etale pro-finite abelian fundamental group of the…

Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.

A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…

This paper formulates a group condition which is enjoyed by absolute Galois groups, and which guarantees that profinite groups satisfying the condition can be approximated as an inverse limit of groups which are profinite analogues of…

It was recently proven by Esnault, Shusterman and the second named author, that the \'etale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend…

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

This is a report of a talk given at the Oberwolfach workshop on "cohomology of finite groups: Interactions and applications" which was held during July 25th - July 31st, 2010. It is an announcement of some of the results (with motivation)…

We point out some minor errors in a paper by the first author, and explain why they do not affect the main results in the paper.

This document is an expanded version of a lecture presented at a conference on "Thin Groups and Superstrong Approximation" held at the Mathematical Sciences Research Institute in February 2012. Superstrong approximation is a criterion on a…

This paper collects many results on galoisian ideals and Galois theory.

A Hamiltonian renormalization group is presented. Such a formulation is relevant for chiralic systems and more appropriate than the Lagrangian formalism. An application to 1D system is presented.

The article is withdrawn. Its content is contained in the final version of arXiv:0805.1634.

We introduce and study a class of field extensions that we call pre-Galois; viz. extensions that become Galois after some linearly disjoint Galois base change. Among them are geometrically Galois extensions of k(T), with k a field:…

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.