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I'm interested in the following construction. Start with derived category of coherent sheaves witch equivalent to derived category of representations of some dg-algebra. Quasi-isomorphic dg-algebras gives the same "space" (or sheaves on "space") from derived point of view. So I regard $A_\infty$ algebras as natural data for derived non-commutative geometry. So, commutative algebraic constructions have counterparts on $A_\infty$ side. There are explicit description of localization, gluing, blowing up etc. for $A_\infty$ algebras? References are welcome, thanks.

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