Philosophy of contraherent cosheaves
L Positselski - arXiv preprint arXiv:2311.14179, 2023 - arxiv.org
Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …
using the colocalization functors. Contraherent cosheaves are designed to be used for …
Minimal complexes of cotorsion flat modules
P Thompson - arXiv preprint arXiv:1702.02985, 2017 - arxiv.org
Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …
modules to be minimal, in the sense that every self homotopy equivalence is an …
Simplicial presheaves of coalgebras
G Raptis - Algebraic & Geometric Topology, 2013 - msp.org
The category of simplicial ℛ–coalgebras over a presheaf of commutative unital rings on a
small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated …
small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated …
Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory
LW Christensen, S Estrada… - … combinatorial methods in …, 2020 - books.google.com
We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …
Local, colocal, and antilocal properties of modules and complexes over commutative rings
L Positselski - Journal of Algebra, 2024 - Elsevier
This paper is a commutative algebra introduction to the homological theory of quasi-
coherent sheaves and contraherent cosheaves over quasi-compact semi-separated …
coherent sheaves and contraherent cosheaves over quasi-compact semi-separated …
Purity and ascent for Gorenstein flat cotorsion modules
I Bird - arXiv preprint arXiv:2108.08135, 2021 - arxiv.org
The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …
functor which preserves purity and pure injectivity. We consider how this functor behaves …
Gorenstein cotilting and tilting modules
L Yan, W Li, B Ouyang - Communications in Algebra, 2016 - Taylor & Francis
Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …
Adjoint and Frobenius pairs of functors for corings
M Zarouali-Darkaoui - Communications in Algebra®, 2007 - Taylor & Francis
We investigate adjoint and Frobenius pairs between categories of comodules over rather
general corings. We particularize to the case of the adjoint pair of functors associated to a …
general corings. We particularize to the case of the adjoint pair of functors associated to a …
Gorenstein complexes and recollements from cotorsion pairs
J Gillespie - arXiv preprint arXiv:1210.0196, 2012 - arxiv.org
We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
Flat covers in the category of quasi-coherent sheaves over the projective line
E Enochs, S Estrada, JR García Rozas, L Oyonarte - 2004 - Taylor & Francis
In this paper we prove the existence of a flat cover and a cotorsion envelope for any quasi-
coherent sheaf over the projective line, where R is any commutative ring. We first prove a …
coherent sheaf over the projective line, where R is any commutative ring. We first prove a …