Weakly curved A-infinity algebras over a topological local ring
arXiv:1202.2697 · doi:10.24033/msmf.467
Abstract
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.
arXiv commentLaTeX 2e with pb-diagram and xy-pic, 186 pages, 31 commutative diagrams; v.7: references added in sections 0.11 and 0.12, explanations added in section 1.4, remarks 1.2.2-1.2.4 and 5.3.4 inserted, three paragraphs converted into propositions in sections 1.6 and 1.7, visual appearance improved throughout the text; v.8: small changes, many misprints corrected -- this is intended as the final version