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pro vyhledávání: '"Vitória, Jorge"'
Given a presilting object in a triangulated category, we find necessary and sufficient conditions for the existence of a complement. This is done both for classic (pre)silting objects and for large (pre)silting objects. The key technique is the study
Externí odkaz:
http://arxiv.org/abs/2402.13356
Autor:
Vitória, Jorge
The representation theory of a commutative noetherian ring is tightly controlled by its prime spectrum. In this article we use the prime spectrum to describe mutation of cosilting objects in the derived category of a commutative noetherian ring.
Externí odkaz:
http://arxiv.org/abs/2310.01834
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 lattice of torsion pairs in module or derived categories. In this paper we
Externí odkaz:
http://arxiv.org/abs/2201.02147
Autor:
Pavon, Sergio, Vitória, Jorge
Over a commutative noetherian ring $R$, the prime spectrum controls, via the assignment of support, the structure of both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, the assignment of support classifies heredi
Externí odkaz:
http://arxiv.org/abs/2009.08763
Autor:
Vitória, Jorge
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 those same structures. More explicitly, we review the fact that (1) a fi
Externí odkaz:
http://arxiv.org/abs/2001.04730
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 localising subcate
Externí odkaz:
http://arxiv.org/abs/1902.05817
Autor:
Laking, Rosanna, Vitória, Jorge
Publikováno v:
Pacific J. Math. 306 (2020) 557-586
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 conditions involving products, coproducts, directed homotopy colimits an
Externí odkaz:
http://arxiv.org/abs/1811.00340
Publikováno v:
Q. J. Math. 71 (2020), no. 4, 1489-1520
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 localisation in the sense of Cohn and Schofield; and (b) when such universa
Externí odkaz:
http://arxiv.org/abs/1807.01982
We prove that a finite dimensional algebra is $\tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $\tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of basic suppo
Externí odkaz:
http://arxiv.org/abs/1801.04312
Autor:
Parra, Carlos E., Vitória, Jorge
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 paper is dedicated to investigating the behaviour under glueing of som
Externí odkaz:
http://arxiv.org/abs/1710.04632