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

SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY

Speaker:

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.