Related papers: A short note on groups in separably closed valued …

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.

We say that a subgroup $H$ is isolated in a group $G$ if for every $x\in G$ we have either $x\in H$ or $\langle x\rangle\cap H=1$. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used…

In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type "A" over algebraically closed field F of characteristic zero.

Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

Let G be a reductive connected group over the algebraic closure of a finite field. In this paper we give the classification of character sheaves on G in categorical terms (as a categorical centre). Previously such a classification was known…

A note connecting arguments scattered in the extant literature proving that, in any o-minimal expansion of the real field, a definable family of sets has the property that the set of parameters corresponding to finite-volume fibers is…

We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…

We consider metric versions of the notions of local embeddability and LEF. We pay special attention to normally finitely generated groups with word metrics.

In this work, we classify all finite groups such that for every field extension F of \mathbb{Q}, F is the field of values of at most 3 irreducible characters.

Let $G$ be a connected reductive group. We find a necessary and sufficient condition for a quasiaffine homogeneous space of $G$ to be embeddable into an irreducible $G$-module. In addition, for an affine homogeneous space we find a…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…

We prove finiteness properties for groups of homeomorphisms that have finitely many "singular points", and we describe the normal structure of such groups. As an application, we prove that every countable abelian group can be embedded into…

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. \emph{isomorphs}) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…