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Shizhuo Zhang
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Did Durov's work give an example of noncommutative schemes

I just took a look at the nlab entry: Nikolai Durov. It seems that Skoda ever mentioned that what Durov introduced was special case of generalized scheme theory. Because I did not read his dissertation carefully neither completely. I wonder ask whether his "generalized scheme" is special case of noncommutative scheme in the sense of A.Rosenberg.

I will give a talk on noncommutative scheme in a few days. Now I am collecting interesting examples of noncommutative schemes(quasi scheme). Examples that I already knew are:

commutative schemes, D-modules, quantum D-modules, almost schemes by Gabber, general Grothendieck category(abelian category), Artin-Zhang noncommutative projective scheme. Quantum flag variety in the sense of Rosenberg and Lunts. Holonomic D-modules.

Thanks!

Shizhuo Zhang
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  • 59