Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Yuriy Drozd
Affiliation:

Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev/MPIM
Date:

Thu, 31/03/2022 - 15:00 - 16:00 For zoom details contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

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 center and the schemes with the same center are Morita equivalent if and only if one of them is isomorphic to the scheme of endomorphisms of a local progenerator of the other.

It is a common work with Igor Burban.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158