Silting objects
L Angeleri Hügel - Bulletin of the London Mathematical Society, 2019 - Wiley Online Library
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 …
pairs in triangulated categories, we discuss and compare different notions of silting and …
Torsion pairs in silting theory
L Angeleri Hügel, F Marks, J Vitória - Pacific Journal of Mathematics, 2017 - msp.org
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 satisfies …
(co) silting t-structure is a Grothendieck category if and only if the (co) silting object satisfies …
Lifting and restricting t‐structures
F Marks, A Zvonareva - Bulletin of the London Mathematical …, 2023 - Wiley Online Library
We explore the interplay between t‐structures in the bounded derived category of finitely
presented modules and the unbounded derived category of all modules over a coherent ring …
presented modules and the unbounded derived category of all modules over a coherent ring …
Simples in a cotilting heart
L Angeleri Hügel, I Herzog, R Laking - Mathematische Zeitschrift, 2024 - Springer
Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the
derived category D (Mod-R). We determine the simple objects in this heart and their injective …
derived category D (Mod-R). We determine the simple objects in this heart and their injective …
[HTML][HTML] t-Structures on stable derivators and Grothendieck hearts
We prove that, given any strong and stable derivator and a t-structure in its base triangulated
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …
Torsion pairs over n-hereditary rings
D Bravo, CE Parra - Communications in Algebra, 2019 - Taylor & Francis
We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …
Locally finitely presented and coherent hearts
Starting with a Grothendieck category $\mathcal {G} $ and a torsion pair $\mathbf
{t}=(\mathcal {T},\mathcal {F}) $ in $\mathcal G $, we study the local finite presentability and …
{t}=(\mathcal {T},\mathcal {F}) $ in $\mathcal G $, we study the local finite presentability and …
Locally finitely presented and coherent hearts
Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …
Universal co-extensions of torsion abelian groups
A Argudín-Monroy, CE Parra - Journal of Algebra, 2024 - Elsevier
Abstract In [16], a theory of universal extensions in abelian categories is developed; in
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …
Local coherence of hearts in the derived category of a commutative ring
L Martini - 2022 - iris.unitn.it
Approximation theory is a fundamental tool in order to study the representation theory of a
ring R. Roughly speaking, it consists in determining suitable additive or abelian …
ring R. Roughly speaking, it consists in determining suitable additive or abelian …