Abstract
Let X be a scheme over an abelian symmetric monoidal category (C,⊗,1) satisfying certain conditions. In this article, we develop the theory of the derived category D(OX−QCoh) of quasi-coherent sheaves on X (where X is not necessarily noetherian). In particular, we show the following two results: (1) the category D(OX−QCoh) carries a derived tensor product and contains internal hom objects, and (2) let Δ(X) be the smallest triangulated subcategory of D(OX−QCoh) containing all the objects j⁎M•, where j:U⟶X is an open immersion with U affine and M•∈D(OU−QCoh). Then, Δ(X)=D(OX−QCoh).
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