41 citations · 89 across the 9 of their papers we have counts for
14 papers
Mutation and torsion pairs
Lidia Angeleri Hügel, Rosanna Laking, Jan Šťovíček +1
Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the latti…
Hearts for commutative noetherian rings: torsion pairs and derived equivalences
Sergio Pavon, Jorge Vitória
Over a commutative noetherian ring , the prime spectrum controls, via the assignment of support, the structure of both and . We show that, just…
Quantity vs. size in representation theory
Jorge Vitória
In this note, we survey two instances in the representation theory of finite-dimensional algebras where the quantity of a type of structures is intimately related to the size of th…
Partial silting objects and smashing subcategories
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
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…
Definability and approximations in triangulated categories
Rosanna Laking, Jorge Vitória
We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure co…
Flat ring epimorphisms and universal localisations of commutative rings
Lidia Angeleri Hügel, Frederik Marks, Jan Stovicek +2
We study different types of localisations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal local…
A characterisation of -tilting finite algebras
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
We prove that a finite dimensional algebra is -tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a -tilting finite algebra …
Properties of abelian categories via recollements
Carlos E. Parra, Jorge Vitória
A recollement is a decomposition of a given category (abelian or triangulated) into two subcategories with functorial data that enables the glueing of structural information. This…
Silting and cosilting classes in derived categories
Frederik Marks, Jorge Vitória
An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bou…
Torsion pairs in silting theory
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
In the setting of compactly generated triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and only if the (co)silting object…
Silting modules and ring epimorphisms
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every…
Silting modules
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support -tilting modules over a finite dimensional a…
t-structures via recollements for piecewise hereditary algebras
Qunhua Liu, Jorge Vitória
Following the work of Beilinson, Bernstein and Deligne, we study restriction and induction of t-structures in triangulated categories with respect to recollements. For derived cate…
Mutations Vs. Seiberg duality
Jorge Vitória
For a quiver with potential, Derksen, Weyman and Zelevinsky defined a combinatorial transformation - mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seib…