Related papers: Tannakian Fundamental Groups Associated to Galois …

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…

In this paper, we construct, for some $2$-groups $G$, explicit Galois extensions $E/\mathbb{Q}(T)$ of group $G$ with $E\cap\overline{\mathbb{Q}}=\mathbb{Q}$. We also provide explicit arithmetic progressions of integers $t_0$ such that the…

We define a linear structure on Grothendieck's arithmetic fundamental group $\pi_1(X, x)$ of a scheme $X$ defined over a field $k$ of characteristic 0. It allows us to link the existence of sections of the Galois group ${\rm Gal}(\bar k/k)$…

Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the equivariant connection theory and holonomy of such…

In this paper we produce unconditionally new instances of Galois number field extensions exhibiting strong discrepancies in the distribution of Frobenius elements among conjugacy classes of the Galois group. We first prove an inverse Galois…

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

This paper surveys some results and methods in topological transformation groups.

We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…

This is a revised version (replacing an older one) with typos fixed and the introduction expanded.

In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.

In this short note we introduce the unconditional noncommutative motivic Galois groups and relate them with those of Andre-Kahn.

In this note we study the finite groups whose subgroup lattices are dismantlable.

This is the third and last of three papers containing the complete proof that all finitely presented groups are QSF.

Let $k$ be an algebraically closed field of characteristic zero, $F$ be an algebraically closed extension of $k$ of transcendence degree one, and $G$ be the group of automorphisms over $k$ of the field $F$. The purpose of this note is to…

Let $X$ be a reduced connected $k$-scheme pointed at a rational point $x \in X(k)$. By using tannakian techniques we construct the Galois closure of an essentially finite $k$-morphism $f:Y\to X$ satisfying the condition…

Galois categories can be viewed as the combinatorial analog of Tannakian categories. We introduce the notion of pre-Galois category, which can be viewed as the combinatorial analog of pre-Tannakian categories. Given an oligomorphic group…

This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.

This is the written version of the Bourbaki seminar given in January 2013 and published in 2014 (modulo an additional early reference added subsequently). It describes the first construction of infinite, finitely generated amenable simple…

We give a complete answer to the analogue of Grothendieck conjecture on p-curvatures for q-difference equations defined over K(x), where K is any finitely generated extension of Q and q\in K can be either a transcendental or an algebraic…

This is the first in a sequence of papers that will develop the theory of automorphisms of nonsolvable finite groups. The sequence will culminate in a new proof of McBride's Nonsolvable Signalizer Functor Theorem, which is one of the…