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New entries Kapranov's noncommutative geometry and Dmitry Kaledin. New references and typographic improvements at noncommutative algebraic geometry.
Orlov's reference on completions to formal geometry and Dmitri Orlov. It says a bit about how to see the completion of a ringed subspace from the point of view of the derived category of sheaves and its subcategory/quotient category. Formal thickenings at abelian level are considered in Lunts-Rosenberg MPI 1996 preprint (link at Alexander Rosenberg). A cartesian property of completions is in our paper with Durov.
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