Date and Time: Monday 26 October, 11.30am
Speaker: Omkar Javadekar
Google Meet link:
https://meet.google.com/afe-nzqz-sgt
Title: Serre’s conjecture for projective modules
Abstract: Also known as Quillen-Suslin theorem, Serre's conjecture is a result concerning the
relationship between free and projective modules over polynomial rings. It states that every finitely
generated projective module over a polynomial ring over a field is free. The statement was conjectured
by Serre in 1955, and the first proofs were given independently by Quillen and Suslin in 1976. In this
talk we will see a proof of Serre's conjecture.
We begin by defining unimodular extension property. We then show that polynomial rings have unimodular extension property. Finally, appealing to the result that finitely generated projective modules over polynomial rings are stably free, we conclude the proof of Serre's conjecture by showing that stably free modules over a ring having unimodular extension property are free.