相关论文: Residual regularity in tensor triangular geometry

Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field k. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of k…

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…

These are the notes from lectures I gave at the Oberwolfach Seminar "Tensor Triangular Geometry and Interactions" which was held in October 2025. The aim of these notes is twofold: We develop notions of support for triangulated categories,…

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…

The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…

We propose a general method to construct new triangulated categories, relative stable categories, as additive quotients of a given one. This construction enhances results of Beligiannis, particularly in the tensor-triangular setting. We…

Residual finiteness growth gives an invariant that indicates how well-approximated a finitely generated group is by its finite quotients. We briefly survey the state of the subject. We then improve on the best known upper and lower bounds…

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations…

We define and discuss some general properties of residual categories of Lefschetz decompositions in triangulated categories. In the case of the derived category of coherent sheaves on the Grassmannian $\text{G}(k,n)$ we conjecture that the…

We give a characterisation of those local not necessary commutative rings, for which the category of projective modules admits a triangulation with the identity as translation functor. By "admits a triangulation" we mean that the category…

We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We introduce the notion of pure descendability and we apply it…

On objects of a triangulated category with a stability condition, we construct a topology.

Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

We survey some methods developed in a series of papers, for classifying localising subcategories of tensor triangulated categories. We illustrate these methods by proving a new theorem, providing such a classification in the case of the…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

The goal of this note is to provide a recursive algorithm that allows one to calculate the expansion of the metric tensor up to the desired order in Riemann normal coordinates. We test our expressions up to fourth order and predict results…

We show several properties related to the structure of the family of classes of two-dimensional periodic continued fractions. This approach to the study of the family of classes of nonequivalent two dimexsional periodic continued fractions…