nLab noncommutative projective geometry

The noncommutative projective geometry is a name of several directions in noncommutative algebraic geometry. The noncommutative projective schemes are supposed to be represented with noncommutative \mathbb{N}-graded algebras; as in commutative case, different graded algebras may give rise to the isomorphic schemes. By definition the category QcohProjAQcoh Proj A of quasicoherent sheaves over the ProjProj of a noncommutative graded algebra AA is the full category of (say left) modules grMod AgrMod_A modulo the torsion subcategory of the category of modules of finite length.

Most often one limits to noncommutative algebras which are close to commutative in certain sense. One very usable axiomatics is due Artin and Zhang and has been widely used:

  • M. Artin, J. J. Zhang, Noncommutative projective schemes, Adv. Math. 109 (1994), no. 2, 228-287, MR96a:14004, doi

Last revised on March 6, 2013 at 19:06:27. See the history of this page for a list of all contributions to it.