Weakly curved A-infinity algebras over a topological local ring

0505597 - MÚ 2020 RIV FR eng B - Monography
Positselski, Leonid
Weakly curved A-infinity algebras over a topological local ring.
1. - Marseille: Société Mathématique France, 2018. 206 s. Mémoires de la Société Mathématique de France. Nouvelle Série, 159. ISBN 978-2-85629-899-2. ISSN 0249-633X
Institutional support: RVO:67985840
Keywords : bar-cobar duality * contramodules and comodules * Floer-Fukaya theory
OECD category: Pure mathematics
https://smf.emath.fr/publications/weakly-curved-ainfty-algebras-over-topological-local-ring

We define and study the derived categories of the first kind for curved DG and A-infinity algebras complete over a pro-Artinian local ring with the curvature elements divisible by the maximal ideal of the local ring. We develop the Koszul duality theory in this setting and deduce the generalizations of the conventional results about A-infinity modules to the weakly curved case. The formalism of contramodules and comodules over pro-Artinian topological rings is used throughout the paper. Our motivation comes from the Floer-Fukaya theory.
Permanent Link: http://hdl.handle.net/11104/0297064