Partial silting objects and smashing subcategories

Hügel, Lidia Angeleri; Marks, Frederik; Vitória, Jorge

doi:10.1007/s00209-019-02450-2

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…The case of a large presilting object will be discussed in a forthcoming paper by Angeleri Hügel, Pauksztello and Vitória. The paper will be devoted to partial silting objects. It will be shown that in the derived category

D (A)

of an arbitrary ring

A

every set

Σ \subset {sans-serifK}^{b} false(proj (A) false)

of compact objects admits a partial silting object

T

such that

{normalΣ}^{⊥_{Z}} = T^{⊥_{Z}}

, in analogy with a result for two‐term complexes from .…”

Section: Classification Resultsmentioning

confidence: 99%

Silting Objects

Hügel

2019

Bull. London Math. Soc.

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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 co-t-structures. We then focus on silting and cosilting objects in a triangulated category with coproducts and study the case of the unbounded derived category of a ring. We close the survey with some classification results over commutative Noetherian rings and silting-discrete algebras. Contents

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D (A)

of an arbitrary ring

A

every set

Σ \subset {sans-serifK}^{b} false(proj (A) false)

of compact objects admits a partial silting object

T

such that

{normalΣ}^{⊥_{Z}} = T^{⊥_{Z}}

, in analogy with a result for two‐term complexes from .…”

Section: Classification Resultsmentioning

confidence: 99%

Silting Objects

Hügel

2019

Bull. London Math. Soc.

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T-structures on unbounded twisted complexes

Genovese

2023

Math. Z.

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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 interesting in the case of dg-categories of derived injectives or derived projectives associated to a t-structure. On such unbounded twisted complexes we define a natural “injective” and dually a “projective” t-structure. This is intended as a direct generalization of the homotopy categories of injective or projective objects of an abelian category.

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When Is the Silting-Discreteness Inherited?

AIHARA,

HONMA

2024

Nagoya Math. J.

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We explore when the silting-discreteness is inherited. As a result, one obtains that taking idempotent truncations and homological epimorphisms of algebras transmit the silting-discreteness. We also study classification of silting-discrete simply-connected tensor algebras and silting-indiscrete self-injective Nakayama algebras. This paper contains two appendices; one states that every derived-discrete algebra is silting-discrete, and the other is about triangulated categories whose silting objects are tilting.

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Partial silting objects and smashing subcategories

Cited by 3 publications

References 39 publications

Silting Objects

Silting Objects

T-structures on unbounded twisted complexes

When Is the Silting-Discreteness Inherited?

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