scholarly journals The stable category of Gorenstein flat sheaves on a noetherian scheme

2020 ◽  
pp. 1
Author(s):  
Lars Winther Christensen ◽  
Sergio Estrada ◽  
Peder Thompson
Keyword(s):  
Stable Category ◽  
Noetherian Scheme ◽  
Gorenstein Flat

Buchweitz’s equivalences for Gorenstein flat modules with respect to semidualizing modules

2019 ◽  
pp. 2150006
Author(s):  
Jiangsheng Hu ◽  
Yuxian Geng ◽  
Jinyong Wu ◽  
Huanhuan Li
Keyword(s):  
Noetherian Ring ◽  
Full Subcategory ◽  
Stable Category ◽  
Commutative Noetherian Ring ◽  
Singularity Category ◽  
Flat Modules ◽  
Frobenius Category ◽  
Semidualizing Modules ◽  
Structure Formula ◽  
Gorenstein Flat

Let [Formula: see text] be a commutative Noetherian ring and [Formula: see text] a semidualizing [Formula: see text]-module. We obtain an exact structure [Formula: see text] and prove that the full subcategory [Formula: see text] of [Formula: see text] is a Frobenius category with [Formula: see text] the subcategory of projective and injective objects, where [Formula: see text] and [Formula: see text] (respectively, [Formula: see text]) is the subcategory of [Formula: see text]-Gorenstein flat (respectively, [Formula: see text]-flat [Formula: see text]-cotorsion) [Formula: see text]-modules. Then the stable category [Formula: see text] of [Formula: see text] and the singularity category [Formula: see text] of [Formula: see text] are also considered. As a consequence, we get that there is a Buchweitz’s equivalence [Formula: see text] if and only if [Formula: see text] is a part of some AB-context.

scholarly journals Gorenstein flat representations of left rooted quivers

2021 ◽  
Author(s):  
Zhenxing Di ◽  
Sergio Estrada ◽  
Li Liang ◽  
Sinem Odabaşı
Keyword(s):  
Gorenstein Flat

scholarly journals On Gorenstein Flat Preenvelopes of Complexes

2013 ◽  
Vol 129 ◽  
pp. 171-187 ◽  
Author(s):  
Gang Yang ◽  
Zhongkui Liu ◽  
Li Liang
Keyword(s):  
Gorenstein Flat

Noncommutative G-semihereditary rings

2018 ◽  
Vol 17 (01) ◽  
pp. 1850014 ◽  
Author(s):  
Jian Wang ◽  
Yunxia Li ◽  
Jiangsheng Hu
Keyword(s):  
Associative Ring ◽  
Sufficient Condition ◽  
Projective Modules ◽  
The Third ◽  
Flat Modules ◽  
Gorenstein Projective Modules ◽  
Direct Limits ◽  
Gorenstein Flat ◽  
Finitely Presented ◽  
Semihereditary Rings

In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [Formula: see text] is a commutative ring. Some new characterizations of left [Formula: see text]-semihereditary rings are given. Applications go in three directions. The first is to give a sufficient condition when a finitely presented right [Formula: see text]-module is Gorenstein flat if and only if it is Gorenstein projective provided that [Formula: see text] is left coherent. The second is to investigate the relationships between Gorenstein flat modules and direct limits of finitely presented Gorenstein projective modules. The third is to obtain some new characterizations of semihereditary rings, [Formula: see text]-[Formula: see text] rings and [Formula: see text] rings.

Separable monoids in Dqc (X)

2018 ◽  
Vol 2018 (738) ◽  
pp. 237-280 ◽  
Author(s):  
Amnon Neeman
Keyword(s):  
Triangulated Category ◽  
Noetherian Scheme ◽  
Structure Sheaf ◽  
Tensor Triangulated Category

AbstractSuppose{({\mathscr{T}},\otimes,\mathds{1})}is a tensor triangulated category. In a number of recent articles Balmer defines and explores the notion of “separable tt-rings” in{{\mathscr{T}}}(in this paper we will call them “separable monoids”). The main result of this article is that, if{{\mathscr{T}}}is the derived quasicoherent category of a noetherian schemeX, then the only separable monoids are the pushforwards by étale maps of smashing Bousfield localizations of the structure sheaf.

Notes on Gorenstein Flat Modules

2018 ◽  
Vol 45 (2) ◽  
pp. 337-344
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan
Keyword(s):  
Flat Modules ◽  
Gorenstein Flat

Complete Intersection Flat Dimension and the Intersection Theorem

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1161-1166
Author(s):  
Parviz Sahandi ◽  
Tirdad Sharif ◽  
Siamak Yassemi
Keyword(s):  
Local Ring ◽  
Complete Intersection ◽  
Intersection Theorem ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Gorenstein Dimension ◽  
Flat Dimension ◽  
Gorenstein Flat ◽  
Similar Extension

Any finitely generated module M over a local ring R is endowed with a complete intersection dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension can be extended to all modules over the ring R. This paper presents a similar extension for the complete intersection dimension, and mentions the relation between this dimension and the Gorenstein flat dimension. In addition, we show that in the intersection theorem, the flat dimension can be replaced by the complete intersection flat dimension.

scholarly journals The projective stable category of a coherent scheme

2018 ◽  
Vol 149 (1) ◽  
pp. 15-43 ◽  
Author(s):  
Sergio Estrada ◽  
James Gillespie
Keyword(s):  
Homotopy Category ◽  
Model Structure ◽  
Stable Category ◽  
Coherent Sheaves ◽  
Chain Complexes

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model structure, which are certain complexes of flat quasi-coherent sheaves satisfying a special acyclicity condition.

Gorenstein flat modules relative to injectively resolving subcategories

2021 ◽  
pp. 2250099
Author(s):  
Zenghui Gao ◽  
Wan Wu
Keyword(s):  
Homological Dimension ◽  
Common Generalization ◽  
Flat Modules ◽  
Resolving Subcategory ◽  
Homological Dimensions ◽  
Gorenstein Flat

Let [Formula: see text] be an injectively resolving subcategory of left [Formula: see text]-modules. We introduce and study [Formula: see text]-Gorenstein flat modules as a common generalization of some known modules such as Gorenstein flat modules (Enochs, Jenda and Torrecillas, 1993), Gorenstein AC-flat modules (Bravo, Estrada and Iacob, 2018). Then we define a resolution dimension relative to the [Formula: see text]-Gorensteinflat modules, investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, stability of the category of [Formula: see text]-Gorensteinflat modules is discussed, and some known results are obtained as applications.

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