t-стабильности и t-структуры на триангулированных категориях

Городенцев, Алексей Львович; Gorodentsev, Alexei Lvovich; Кулешов, Сергей Алексеевич; Kuleshov, Sergej Alekseevich; Рудаков, А. Н.

doi:10.4213/im497

Izv. RAN. Ser. Mat.

2004

DOI: 10.4213/im497

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t-стабильности и t-структуры на триангулированных категориях

Алексей Львович Городенцев¹,

Alexei Lvovich Gorodentsev²,

Сергей Алексеевич Кулешов³

et al.

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Cited by 9 publications

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t-structures on hereditary categories

Stanley

Roosmalen

2018

Math. Z.

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We study aisles in the derived category of a hereditary abelian category. Given an aisle, we associate a sequence of subcategories of the abelian category by considering the different homologies of the aisle. We then obtain a sequence, called a narrow sequence.We then prove that a narrow sequence in a hereditary abelian category consists of a nondecreasing sequence of wide subcategories, together with a tilting torsion class in each of these wide subcategories. Furthermore, there are relations these torsion classes have to satisfy. These results are sufficient to recover known classifications of t-structures for smooth projective curves, and for finitely generated modules over a Dedekind ring.In some special cases, including the case of finite dimensional modules over a finite dimensional hereditary algebra, we can reduce even further, effectively decoupling the different tilting torsion theories one chooses in the wide subcategories.

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t-structures on hereditary categories

Stanley

Roosmalen

2018

Math. Z.

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T-structures on the Bounded Derived Category of the Kronecker Algebra

Salorio

Trepode

2011

Appl Categor Struct

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t-Structures are Normal Torsion Theories

Fiorenza

Loregian

2015

Appl Categor Struct

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t-стабильности и t-структуры на триангулированных категориях

Cited by 9 publications

References 12 publications

t-structures on hereditary categories

t-structures on hereditary categories

T-structures on the Bounded Derived Category of the Kronecker Algebra

t-Structures are Normal Torsion Theories

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