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Noncommutative geometry in the sense of Connes and beyond: noncommutative algebras viewed as functions on a noncommutative space.
3
votes
K theory long exact sequence
You can combine Adeel Khan's answer with Proposition 6.9 of my paper with David Gepner to prove that there are these kinds of localization sequences in a great deal of generality. (Note that our propo …
3
votes
Bimodules in geometry
In a paper from 1985, Raeburn and J. Taylor describe how to view all elements of H^2(X,Gm) (etale cohomology) as coming from non-unital Azumaya algebras. The construction relies on bimodule theory for …