Related papers: Tannakian Fundamental Groups Associated to Galois …

We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115}…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.

A summary of new experimental results and recent theoretical developments discussed in the "Hadronic Final States and QCD" working group is presented.

This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.

This paper introduces a notion of fundamental group appropriate for laminations.

This paper surveys the methods that have been used to attack the conjecture, still open, that an abelian variety over a characteristic $0$ field with finitely generated Galois group is always of infinite rank.

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we…

We establish the faithfulness of a geometric action of the absolute Galois group of the rationals that can be defined on the discriminantal variety associated to a finite complex reflection group, and review some possible connections with…

In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem. In this paper, we completely…

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

The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no…

This is the final version of a book about p-adic families of Galois representations, Selmer groups, eigenvarieties and Arthur's conjectures

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group lattice, studied in our previous papers \cite{8} and \cite{9}. A…

This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…

This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.