Related papers: On complexes of finite complete intersection dimen…
We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings.…
This paper aims to give some examples of diffeomorphic (or homeomorphic) low-dimensional complete intersections, which can be considered as a geometrical realization of classification theorems about complete intersections. A conjecture of…
How small can a set be while containing many configurations? Following up on earlier work of Erd\H os and Kakutani \cite{MR0089886}, M\'ath\'e \cite{MR2822418} and Molter and Yavicoli \cite{Molter}, we address the question in two…
If an element of the Grothendieck group of the derived category of a scheme is locally represented by perfect complexes, then can the original element be represented by a perfect complex? We provide a counterexample on a projective variety…
We study random, finite-dimensional, ungraded chain complexes over a finite field and show that for a uniformly distributed differential a complex has the smallest possible homology with the highest probability: either zero or…
We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…
Any superrosy division ring (i.e. a division ring equipped with an abstract notion of rank) is shown to be centrally finite. Furthermore, division rings satisfying a generalized chain condition on definable subgroups are studied. In…
Groups of almost upper triangular infinite matrices with entries indexed by integers are studied. It is shown that, when the matrices are over a finite field, these groups admit a nondiscrete totally disconnected, locally compact group…
This paper proves the existence of homeomorphic (diffeomorphic) complex 6-dimensional (7-dim) complete intersections that belong to components of the moduli space of different dimensions. These results are given as a supplement to earlier…
For Y a closed normal subvariety of codimension c of a smooth complex variety X, Brylinski and Kashiwara showed that the local cohomology module H^c_Y(X,O_X) contains a unique simple D_X-submodule, denoted by L(Y,X). In this paper the…
Let $R$ be a commutative ring. A full additive subcategory $\C$ of $R$-modules is triangulated if whenever two terms of a short exact sequence belong to $\C$, then so does the third term. In this note we give a classification of…
We compute the Balmer spectrum of the category of perfect complexes on an algebraic stack admitting a finite locally free cover by an affine scheme and identify it with the homogeneous spectrum of the cohomology ring.
We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the…
We establish that for q>=1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of…
Complete intersections may be unexpectedly simple over fields of positive characteristic: for instance, they may be unirational despite being of general type. One explanation is given by profiles, structure that tracks the special shape of…
In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…
Let $(R,\fm)$ be commutative Noetherian local ring. It is shown that $R$ is Cohen--Macaulay ring if there exists a Cohen--Macaulay finite (i.e. finitely generated) $R$--module with finite upper Gorenstein dimension. In addition, we show…