Morita theorem gives a criterion of equivalence of categories of modules over rings. On the other hand, Gabriel proved that the category of coherent sheaves defines a Noetherian scheme up to isomorphism. We have established a result which is in a sense, a union and a combination of these two theorems. Namely, we show that the category of coherent sheaves over a Noetherian non-commutative scheme completely defines its centre and the schemes with the same centre are Morita equivalent if and only if one of them is isomorphic to the scheme of endomorphisms of a local progeneretor of the other.
This is joint work with Igor Burban.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
