Koszul-Tate resolutions as cofibrant replacements of algebras over differential operators

DOI10.1007/s40062-018-0202-xzbMath1423.18056arXiv1801.03770OpenAlexW3100758569WikidataQ130066294 ScholiaQ130066294MaRDI QIDQ1630580

Gennaro Di Brino, Damjan Pištalo, Norbert Poncin

Publication date: 10 December 2018

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.03770

zbMATH Keywords

differential operatorBatalin-Vilkovisky formalismmodel category\(\mathcal{D}\)-modulefunctor of pointshomotopical geometry\(\mathcal{D}\)-geometryKoszul-Tate resolutionrelative Sullivan \(\mathcal{D}\)-algebra

Mathematics Subject Classification ID

Resolutions; derived functors (category-theoretic aspects) (18G10) Sheaves of differential operators and their modules, (D)-modules (32C38) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Differential graded algebras and applications (associative algebraic aspects) (16E45) Rings of differential operators (associative algebraic aspects) (16S32)

Related Items (8)

A new approach to model categorical homotopy fiber sequences ⋮ Homotopical algebraic context over differential operators ⋮ Gauge PDE and AKSZ‐type Sigma Models ⋮ Unnamed Item ⋮ Linear \(\mathbb{Z}_2^n\)-manifolds and linear actions ⋮ Products in the category of 𝕑2n-manifolds ⋮ The Schwarz-Voronov embedding of \(\mathbb{Z}_2^n\)-manifolds ⋮ Local forms of morphisms of colored supermanifolds

Cites Work

• Homology of Noetherian rings and local rings
• \(D\)-modules, perverse sheaves, and representation theory. Translated from the Japanese by Kiyoshi Takeuchi
• Remarks on two approaches to the horizontal cohomology: Compatibility complex and the Koszul--Tate resolution
• Homotopical algebra
• The flat model structure on complexes of sheaves
• On Koszul–Tate resolutions and Sullivan models
• Homotopical algebraic geometry. II. Geometric stacks and applications
• Hopf Algebras and Generalizations
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