# nLab schematic algebra

## Motivation

The functor $Proj$ of a graded commutative algebra is a projective variety. Projective schemes? are particular cases of schemes, so they have nontrivial covers by open affine subschemes. In the noncommutative case, Ore localizations (even on one-sided Ore sets) on Ore sets which are multiplicatively generated by finite subsets behave very much like Zariski-open subsets. F. van Oystaeyen produced an appropriate notion of a cover in terms of Ore localizations at two-sided Ore subsets in a graded algebra to define a notion of schematic algebra.

…to be written

## Literature

• F. van Oystaeyen, Algebraic geometry for associative algebras, 287 p. Dekker, 2000.

• F. van Oystaeyen, L. Willaert, Cohomology of schematic algebras, J. algebra 185:1 (1996), p. 74–84

• F. van Oystaeyen, L. Willaert, Grothendieck topology, coherent sheaves and Serre’s theorem for schematic algebras, J. Pure and Appl. Algebra, 104 (1995), p. 109–122

• F. van Oystaeyen, L. Willaert, The quantum site of a schematic algebra, Comm. Alg. 24:1(1996), p. 209–222

Revised on March 6, 2013 19:08:46 by Zoran Škoda (161.53.130.104)