Related papers: Compactly generated t-structures in the derived ca…

We study the derived categories of small categories over commutative noetherian rings. Our main result is a parametrization of the localizing subcategories in terms of the spectrum of the ring and the localizing subcategories over residue…

This paper is a sequel to "T-structures and twisted complexes on derived injectives" by the same author with W. Lowen and M. Van den Bergh. We define a dg-category of unbounded twisted complexes on a dg-category, which is particularly…

We study aisles in the derived category of a hereditary abelian category. Given an aisle, we associate a sequence of subcategories of the abelian category by considering the different homologies of the aisle. We then obtain a sequence,…

We consider the contraderived category of left contramodules over a right linear topological ring $\mathfrak R$ with a countable base of neighborhoods of zero. Equivalently, this is the homotopy category of unbounded complexes of projective…

We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated…

We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly…

In this paper, we answer a question of Dwyer, Greenlees, and Iyengar by proving a local ring $R$ is a complete intersection if and only if every complex of $R$-modules with finitely generated homology is proxy small. Moreover, we establish…

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 consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we…

We classify bounded t-structures on the category of perfect complexes over a commutative, Noetherian ring of finite Krull dimension, extending a result of Alonso Tarrio, Jeremias Lopez and Saorin which covers the regular case. In…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of…

Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put…

Given a tensor-triangulated category $T$, we prove that every flat tensor-idempotent in the module category over $T^c$ (the compacts) comes from a unique smashing ideal in $T$. We deduce that the lattice of smashing ideals forms a frame.

A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. Functors with this property are said to be algebraically compact. This is a very strong property used in programming semantics which allows one to interpret…

We show that the twisted homogeneous coordinate rings of elliptic curves by infinite order automorphisms have the curious property that every subalgebra is both finitely generated and noetherian. As a consequence, we show that a…

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of…

We show that Krause's recollement exists for any locally coherent Grothendieck category such that its derived category is compactly generated. As a source of such categories, we consider the hearts of intermediate and restrictable…

Over a commutative noetherian ring $R$ of finite Krull dimension, we show that every complex of flat cotorsion $R$-modules decomposes as a direct sum of a minimal complex and a contractible complex. Moreover, we define the notion of a…

We classify the dualizable localizing ideals of rigidly-compactly generated tt-$\infty$-categories that are cohomologically stratified. By definition, these are the localizing ideals that are dualizable with respect to the Lurie tensor…