Supports of intersections of thick subcategories and proxy smallness
Abstract
Let R be a commutative noetherian ring. Let Db(R) be the bounded derived category of finitely generated R-modules. Let X and Y be thick subcategories of Db(R). In this paper, we consider the question asking when the equality Supp(X Y)=Supp X Supp Y holds, and give several answers. As applications, we obtain a characterization of the proxy small subcategories, and classifications of certain thick subcategories.
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