Commutative algebra 64: Gorenstein rings
Channel: Richard E Borcherds
Date: 2020-12-18

This lecture is part of an online course on commutative algebra, following the book
"Commutative algebra with a view toward algebraic geometry" by David Eisenbud.

We give an informal introduction to Gorenstein local rings, which are informally those with good duality properties. We give several examples of rings that are or are not Gorenstein, and sketch a proof that regular local rings are Gorenstein using the Koszul complex. 

The article "On the ubiquity of Gorenstein rings" by Bass (mentioned in the lecture) can be found here: https://doi.org/10.1007/BF01112819 (Unfortunately it is behind a paywall, but most university accounts should be able to access it for free.)

Reading: Section
Exercises: