Zariski-Lipman Conjecture for Module of Derivations - Part 1

Abstract: Zariski conjectured that if the module of derivations of a local ring $R$ at a point on an algebraic variety defined over a field of chararacteristic $0$ is a free $R$-module then $R$ is regular. In these two talks we will survey most of the interesting results proved affirming the conjecture.

Results of Lipman, Scheja-Storch, Becker, Hochster, Steenbrink-van Straten, Flenner, Kallstrom, Biswas-Gurjar-Kolte, and some general results which can be deduced by combining some of these results will be discussed. An interesting proposed counterexample due to Hochster will be introduced. Some unsolved cases in the paper of Biswas-Gurjar-Kolte will be mentioned.

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