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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…
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 …
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…
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…