[HTML][HTML] Models for singularity categories
H Becker - Advances in Mathematics, 2014 - Elsevier
In this article we construct various models for singularity categories of modules over
differential graded rings. The main technique is the connection between abelian model …
differential graded rings. The main technique is the connection between abelian model …
On purity and applications to coderived and singularity categories
J Stovicek - arXiv preprint arXiv:1412.1615, 2014 - arxiv.org
Given a locally coherent Grothendieck category G, we prove that the homotopy category of
complexes of injective objects (also known as the coderived category of G) is compactly …
complexes of injective objects (also known as the coderived category of G) is compactly …
On exact categories and applications to triangulated adjoints and model structures
M Saorín, J Šťovíček - Advances in Mathematics, 2011 - Elsevier
We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …
conditions. This has immediate applications to cotorsion pairs and their relation to the …
Coherent analogues of matrix factorizations and relative singularity categories
AI Efimov, L Positselski - Algebra & Number Theory, 2015 - msp.org
We define the triangulated category of relative singularities of a closed subscheme in a
scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations …
scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations …
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves
J Stovicek - arXiv preprint arXiv:1301.5206, 2013 - arxiv.org
Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …
structures on exact categories and symmetric monoidal exact categories, in some cases …
Support theory via actions of tensor triangulated categories
G Stevenson - Journal für die reine und angewandte Mathematik …, 2013 - degruyter.com
We give a definition of the action of a tensor triangulated category on a triangulated
category. In the case that is rigidly-compactly generated and is compactly generated we …
category. In the case that is rigidly-compactly generated and is compactly generated we …
Hereditary abelian model categories
J Gillespie - Bulletin of the London Mathematical Society, 2016 - academic.oup.com
Hereditary abelian model categories | Bulletin of the London Mathematical Society | Oxford
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Subcategories of singularity categories via tensor actions
G Stevenson - Compositio Mathematica, 2014 - cambridge.org
We obtain, via the formalism of tensor actions, a complete classification of the localizing
subcategories of the stable derived category of any affine scheme that has hypersurface …
subcategories of the stable derived category of any affine scheme that has hypersurface …
Deconstructibility and the Hill lemma in Grothendieck categories
J Šťovíček - Forum Mathematicum, 2013 - degruyter.com
A full subcategory of a Grothendieck category is called deconstructible if it consists of all
transfinite extensions of some set of objects. This concept provides a handy framework for …
transfinite extensions of some set of objects. This concept provides a handy framework for …
Contraherent cosheaves
L Positselski - arXiv preprint arXiv:1209.2995, 2012 - arxiv.org
Contraherent cosheaves are globalizations of cotorsion (or similar) modules over
commutative rings obtained by gluing together over a scheme. The category of contraherent …
commutative rings obtained by gluing together over a scheme. The category of contraherent …