Harvard–MIT Algebraic Geometry Seminar: Morita theory for non-commutative noetherian schemes


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September 20, 2022 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Yuriy Drozd - Institute of Mathematics of the National Academy of Sciences of Ukraine

We prove that the categories of coherent (or, equivalently, of quasi-coherent) sheaves over two noetherian non-commutative schemes X and Y are equivalent if and only if there centers C(X) and C(Y) are isomorphic and there is a local progenerator in the category of coherent sheaves over X whose sheaf of endomorphisms is anti-isomorphic to the inverse image of the structure sheaf of Y under the isomorphism X->Y. To prove it, we combine the classical Morita theorem with the Gabriel’s theory of locally noetherian categories.