scholarly journals Classifying Serre subcategories via atom spectrum

2012 ◽  
Vol 231 (3-4) ◽  
pp. 1572-1588 ◽  
Author(s):  
Ryo Kanda
Keyword(s):  
Serre Subcategories

Cut cotorsion pairs

2021 ◽  
pp. 1-38
Author(s):  
Mindy Huerta ◽  
Octavio Mendoza ◽  
Marco A. Pérez
Keyword(s):  
General Framework ◽  
Abelian Category ◽  
Triangulated Categories ◽  
Finitistic Dimension ◽  
Coherent Sheaves ◽  
Chain Complexes ◽  
Cotorsion Pairs ◽  
Gorenstein Homological Algebra ◽  
Serre Subcategories ◽  
Dimension Conjecture

Abstract We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain subcategories. We also exhibit some connections between cut cotorsion pairs and Auslander–Buchweitz approximation theory, by considering relative analogs for Frobenius pairs and Auslander–Buchweitz contexts. Several applications are given in the settings of relative Gorenstein homological algebra, chain complexes, and quasi-coherent sheaves, as well as to characterize some important results on the Finitistic Dimension Conjecture, the existence of right adjoints of quotient functors by Serre subcategories, and the description of cotorsion pairs in triangulated categories as co-t-structures.

scholarly journals Types of Serre subcategories of Grothendieck categories

2018 ◽  
Vol 508 ◽  
pp. 16-34 ◽  
Author(s):  
Jian Feng ◽  
Pu Zhang
Keyword(s):  
Serre Subcategories

Serre subcategories and the cofiniteness of generalized local cohomology modules with respect to a pair of ideals

2016 ◽  
Vol 26 (06) ◽  
pp. 1267-1282
Author(s):  
Tran Tuan Nam ◽  
Nguyen Minh Tri
Keyword(s):  
Local Cohomology ◽  
Cofinite Modules ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
Serre Subcategories

We study some properties of the generalized local cohomology modules [Formula: see text] of [Formula: see text] with respect to a pair of ideals [Formula: see text] in Serre subcategories. Some results concerning to [Formula: see text]-cofinite modules are also given in this paper.

Serre subcategories of R-mod

1996 ◽  
Vol 24 (9) ◽  
pp. 2877-2886 ◽  
Author(s):  
Francisco F. Raggi ◽  
Carlos J. E. Signoret P.
Keyword(s):  
Serre Subcategories

scholarly journals Melkersson condition on Serre subcategories

2016 ◽  
pp. 1-12
Author(s):  
Reza Sazeedeh ◽  
Rasul Rasuli
Keyword(s):  
Serre Subcategories

Local Cohomology Modules, Serre Subcategories and Derived Functors of Torsion Functors

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1187-1196 ◽  
Author(s):  
K. Khashyarmanesh ◽  
F. Khosh-Ahang
Keyword(s):  
Local Cohomology ◽  
Derived Functor ◽  
Regular Sequences ◽  
Serre Subcategory ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Cohomology Modules ◽  
Exact Sequences ◽  
Serre Subcategories

In this research, by using filter regular sequences, we obtain some exact sequences of right or left derived functors of local cohomology modules. Then we use them to gain some conditions under which a right or left derived functor of some special functors over local cohomology modules belongs to a Serre subcategory. These results can conclude some generalizations of previous results in this context or regain some of them.

Sign in / Sign up

Export Citation Format

Share Document