相关论文: Orlov spectra as a filtered cohomology theory
The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov building on work of A. Bondal-M. van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the…
We propose a new look on triangulated categories, which is based on the second Hochschild cohomology.
We introduced the notion of Orlov spectra of Abelian categories, and study its some properties. In particular, we give precise result of Orlov spectra of algebras with type $\mathbb{A}_{n}$.
We leverage the results of the prequel in combination with a theorem of D. Orlov to yield some results in Hodge theory of derived categories of factorizations and derived categories of coherent sheaves on varieties. In particular, we…
In this paper we relate triangulated category structures to the cohomology of small categories and define initial obstructions to the existence of an algebraic or topological enhancement. We show that these obstructions do not vanish in an…
We introduce a notion of oriented dialgebra and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomology. We also…
In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently observed for surfaces by Huybrechts. In this paper we focus…
The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations…
A theorem of Bondal and Kapranov lifts representations of cohomological functors from semiorthogonal decompositions of triangulated categories. We present a version of this result for triangulated functors. To this end, we introduce…
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…
Expository notes about spectral sequences, filtered spectra, and synthetic spectra. We focus on the $\tau$-formalism as it arises in filtered spectra.
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…
We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of the tensor triangulated spectrum of the Morel-Voevodsky…
It is becoming increasingly difficult for geometers and even physicists to avoid papers containing phrases like `triangulated category', not to mention derived functors. I will give some motivation for such things from algebraic geometry,…
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
In recent work, for a triangulated category $\cT$, the author introduced a topological space $\tSpec(\cT)$ which we call the triangular spectrum of $\cT$ as a tensor-free analog of the Balmer spectrum for a tensor triangulated category. In…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…