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49,40 €We define and study the derived categories of the first kind for curved DG- and A8-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 A8-modules to the weakly curved case. The formalism of contramodules and comodules over pro-Artinian topological rings is used throughout the memoir. Our motivation comes from the Floer-Fukaya theory.
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