Related papers: Multifiltrations
We deal with the category of finitely generated modules over an artin algebra $A$. Recall that an object in an abelian category is said to be a brick provided its endomorphism ring is a division ring. Simple modules are, of course, bricks,…
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…
We introduce the notion of Mukai regularity (M-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and…
We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of…
We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…
Given a noetherian abelian category $\mathcal Z$ of homological dimension two with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian category of modules over $\text{End} (T)^{\textit{op}}$ are related by a sequence of…
In this note, we discuss several aspects of the functoriality of universal abelian factorizations associated to representations of quivers into abelian categories. After recalling the general construction of universal abelian…
Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…
We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech…
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.
Toric prevarieties are non-separated analogues of toric varieties. Perling \cite{Perling_equivariant_sheaves_tor_var} provided a combinatorial description of equivariant quasicoherent sheaves on toric varieties, extending earlier ideas of…
Using the theory of Klyachko filtrations for reflexive sheaves on toric varieties, we give a description of toric foliations and their singularities in terms of combinatorial data. We extend Spicer's results about co-rank one toric…
In commutative algebra, E. Miller and B. Sturmfels defined the notion of multidegree for multigraded modules over a multigraded polynomial ring. We apply this theory to bifiltered modules over the Weyl algebra D. The bifiltration is a…
Quantum bounded extensions of multifiltered algebras are defined, and they are endowed with a new multifiltration. The behavior of the associated multigraded rings is studied. A refiltering process allows to lift homological properties from…
We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties,…
We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional…
We describe the relationship between the notions of $M$-regular sheaf and $GV$-sheaf in the case of abelian varieties. The former is a natural strengthening of the latter, and we provide an algebraic criterion characterizing it among the…
We study groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the notion of holonomy group of a leaf…