Related papers: A note on fundamental group lattices
In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.
The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in…
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
Using notions of homogeneity we give new proofs of M. Artin's algebraicity criteria for functors and groupoids. Our methods give a more general result, unifying Artin's two theorems and clarifying their differences.
In the general context of functorial topologies, we prove that in the lattice of all group topologies on an abelian group, the infimum between the Bohr topology and the natural topology is the profinite topology. The profinite topology and…
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.
We give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf…
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.
This paper is a summary of author's results on finite flat commutative group schemes. The properties of the generic fibre functor are discussed. A complete classification of finite local flat commutative group schemes over mixed…
This is a brief exposition of the mathematical themes that motivate the special programme at the Newton Institute in 2009. It is mostly intended for the general public having mathematical training up to the level of secondary school.
The purpose of this note is to verify that the archimedean multiplicity one theorems shown for orthogonal groups (as well as general linear and unitary groups) in a previous paper of the authors remain valid for special orthogonal groups.…
Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…
Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…
The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we…
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.