Blowing Up of Non-commutative Smooth Surfaces

Introduction Preliminaries on category theory Non-commutative geometry Pseudo-compact rings Cohen-Macaulay curves embedded in quasi-schemes Blowing up a point on a commutative divisor Derived categories The derived category of a non-commutative blowup Some results on graded algebras and their sections Quantum plane geometry Blowing up $n$ points in an elliptic quantum plane Non-cummutative cubic surfaces Appendix A. Two-categories Appendix B. Summary of notations Appendix C. Index of terminology Bibliography.