Related papers: Support varieties - an axiomatic approach

We survey various approaches to axiomatic stable homotopy theory, with examples including derived categories, categories of (possibly equivariant or localized) spectra, and stable categories of modular representations of finite groups. We…

For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the Zariski spectrum of a certain commutative ring of…

For a tensor triangulated category which is well generated in the sense of Neeman, it is shown that the collection of Bousfield classes forms a set. This set has a natural structure of a complete lattice which is then studied, using the…

Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…

We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis, we show that the twisted variety of a module…

We define $n$-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$n$-angulations. We obtain a large class of examples of…

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…

We prove a stronger version of the octahedral axiom in a pre-triangulated category. The proof uses a new lemma about exact sequences in pointed additive categories which is based on a weak converse of the snake lemma.

We introduce higher-order support varieties for pairs of modules over a commutative local complete intersection ring, and give a complete description of which varieties occur as such support varieties. In the context of a group algebra of a…

In this paper we study the cohomology of tensor products of symmetric powers of the cotangent bundle of complete intersection varieties in projective space. We provide an explicit description of some of those cohomology groups in terms of…

In this paper we explain certain systematic differences between algebraic and topological triangulated categories. A triangulated category is algebraic if it admits a differential graded model, and topological if it admits a model in the…

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not…

We give an overview of recent developments in silting theory. After an introduction on torsion pairs in triangulated categories, we discuss and compare different notions of silting and explain the interplay with t-structures and…

We define and study the functorial spectrum for every triangulated tensor category. A reconstruction result for topologically noetherian schemes similar to (and based on) a theorem by Balmer is proved. An alternative proof of the…

This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…

We propose a new look on triangulated categories, which is based on the second Hochschild cohomology.

Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the…

In this short note we show that representation and character varieties of discrete groups can be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf algebras. Such view point has several interesting…

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…