New Foundations for Algebraic Geometry

This project aims to provide new foundations of algebraic geometry using the theory of differential categories. The project expects to generate new knowledge in both algebraic geometry, by providing a novel perspective on the subject, and the theory of differential category, by developing the concept of schemes relative to differential categories. Expected outcomes include providing a novel unifying theory of the various models of algebraic geometry, and will also allow for the development of new models of algebraic geometry without starting from scratch. This should provide significant benefits, such as generating novel applications of algebraic geometry in fields with differential category applications, specifically in computer science.