Related papers: Triangular objects and systematic K-theory
We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable…
We analyze the BGG Category $\mathcal{O}$ over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a "triangular" GWA for which Category $\mathcal{O}$ decomposes into a direct sum of subcategories, we study in…
Zhou defined $\delta$-semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the semilocal…
We study integrality over rings (all commutative in this paper) and over ideal semifiltrations (a generalization of integrality over ideals). We begin by reproving classical results, such as a version of the "faithful module" criterion for…
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding…
Grothendieck polynomials are important objects in the study of the $K$-theory of flag varieties. Their many remarkable properties have been studied in the context of algebraic geometry and tableaux combinatorics. We explore a new tool,…
We show that the twisted K-theory of the classifying space of a p-local finite group is isomorphic to the completion of the Grothendieck group of twisted representations of the fusion system with respect to the augmentation ideal of the…
We build on previous work on multirings (\cite{roberto2021quadratic}) that provides generalizations of the available abstract quadratic forms theories (special groups and real semigroups) to the context of multirings…
We show that the category of graded modules over a finite-dimensional graded algebra admitting a triangular decomposition can be endowed with the structure of a highest weight category. When the algebra is self-injective, we show…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
We give a classification of all exact structures on a given idempotent complete additive category. Using this, we investigate the structure of an exact category with finitely many indecomposables. We show that the relation of the…
This paper studies the basic K-theoretic properties of a triangulated persistence category (TPC). This notion was introduced in our earlier papers on triangulation, persistence, and Fukaya categories (arXiv:2304.01785 and arXiv:2104.12258)…
The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…
Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…
Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathcal{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the singularity category…
Given a bounded-above cochain complex of modules over a ring, it is standard to replace it by a projective resolution, and it is classical that doing so can be very useful. Recently, a modified version of this was introduced in triangulated…
We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…
We prove that graded K-theory is universal among oriented Borel-Moore homology theories with a multiplicative periodic formal group law.
We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…