Related papers: Problems about torsors over regular rings (with an…

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…

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…

We extend the study of Hall algebras and edge contractions by generalizing Yiqiang Li's work to contraction along vertices with multiple edges. Using the edge contractions, we establish new embeddings among Hall algebras in this broader…

The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…

This survey paper introduces to a technique called Torsion Subcomplex Reduction (TSR) for computing torsion in the cohomology of discrete groups acting on suitable cell complexes. TSR enables one to skip machine computations on cell…

Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theories, the definition has been extended to general…

We compare the obstruction classes defined in arXiv:1101.4069 to those defined by Illusie. We also give sheaf theoretic proofs of some of the standard properties of the cotangent complex.

This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…

This is a survey on the Farrell-Jones Conjecture about the algebraic K- and L-theory of groups rings and its applications to algebra, geometry, group theory, and topology.

We extend the notion of rational points and cohomological obstructions on varieties to categories fibred in groupoids. We also establish the generalized theory of descent by torsors. Then we interpret the obstruction given by the second…

We deal with the rigidity conjecture of symbolic powers over regular rings. This was asked by Huneke. Along with our investigation, we confirm a conjecture [7, Conjecture 3.8].

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…

There are 26 possibilities for the torsion group of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with given torsion group which give the current records for most of the torsion…

Weakly stable torsion classes were introduced by the author and Yekutieli to provide a torsion theoretic characterisation of the notion of weak proregularity from commutative algebra. In this paper we investigate weakly stable torsion…

The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to…

We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

Firstly, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules over an arbitrary ring. Later, under suitable assumptions on the lattice of the…

We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative…

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…