On a conjecture of Vasconcelos - Part 1

Abstract: These two talks are about the following theorem: If I is an ideal of finite projective dimension in a ring $R,$ and the conormal module $I/I^2$ has finite projective dimension over R/I, then I is locally generated by a regular sequence. This was conjectured by Vasconcelos, after he and (separately) Ferrand established the case that the conormal module is projective.

The key tool is the homotopy Lie algebra, an object sitting at the centre of a bridge between commutative algebra and rational homotopy theory. In the first part I will explain what the homotopy Lie algebra is, and how it can be constructed by differential graded algebra techniques, following the work of Avramov. In the second part I will bring all of the ingredients together and, hopefully, present the proof of Vasconcelos' conjecture.

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