Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori

Abstract

The first part of these notes gives an introduction to noncommutative projective geometry after Artin--Zhang. The second part provides an overview of the work of Polishchuk that reconciles noncommutative two-tori having real multiplication with the Artin--Zhang setting.Comment: Final version - exposition improved; a proof of the derived equivalence added (Prop. 3.8). To appear in the proceedings volume of the "International Workshop on Noncommutative Geometry", IPM, Tehran 200