ABSTRACT

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theor

chapter |4 pages

Introduction

chapter 1|48 pages

The Noncommutative Site

chapter 2|50 pages

Structure Sheaves and their Sections

chapter 3|36 pages

Regular Algebras

chapter 4|50 pages

Valuations and Divisors

chapter 5|18 pages

Cohomology Theories

chapter 6|36 pages

A Functorial Approach

chapter 7|28 pages

Formalizing the Topology