Quillen $K$-Theory: A reclamation in Commutative Algebra - Part 2

Abstract: In these two talks I take a pedagogic approach to Quillen $K$-theory. What it takes to teach (and learn) Quillen $K$-theory? I am at the tail end of completing a book on this, which would eventually be available through some outlet. This is based on a course I taught. Current version has nearly 400 pages, in eleven chapters. I finish with Swan’s paper on quadrics. I tried to do it in a reader friendly way, and tried to avoid expressions like “left to the readers”. I would give an overview and a road map.  To justify the title, let me remind you that $K$-theory used to be part of Commutative algebra. In this endeavor, I consolidate the background needed, in about 100 pages, for a commutative algebraist to pick up the book and give a course, or learn. There is a huge research potential in this direction. This is because, with it, topologists have done what they are good at. However, these higher $K$-groups have not been descried in a tangible manner. That would be the job of commutative algebraist, and would require such expertise.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home