On Koszul–Tate resolutions and Sullivan models

2017/08/20 by Damjan Pištalo, Damjan Pistalo, Norbert Poncin
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Differential (mechanical device) #Differential geometry #Frame (networking) #Geometry #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Physics #Programming language #Pure mathematics #Resolution (logic) #math-ph #math.MP

paper · pdf · doi:10.4064/dm779-1-2018

published as Dissertationes Math. 531 (2018), 1-71

arxiv created 2017/08/20 · crossref issued 2018/01/01 · crossref published 2018/01/01 · crossref published-online 2018/01/01 · openalex publication_date 2018/01/01 · crossref created 2018/05/23 · crossref deposited 2018/06/14 · arxiv updated 2018/11/06 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/08/05

Abstract

We report on Koszul–Tate resolutions in algebra, mathematical physics, cohomological analysis of PDEs, and homotopy theory. Further, we define an abstract Koszul–Tate resolution in the frame of D-geometry, i.e., geometry over differential oper

Citations

• D-Modules, Perverse Sheaves, and Representation Theory
• Quantization of Gauge Systems
• Model categorical Koszul-Tate resolution for algebras over differential operators
• Homological Methods in Equations of Mathematical Physics
• Infinitesimal computations in topology
• Local BRST cohomology in gauge theories
• Model structure on differential graded commutative algebras over the ring of differential operators
• Homotopical algebraic context over differential operators
• The (secret?) homological algebra of the Batalin-Vilkovisky approach