By Linquan Ma
The Briançon-Skoda theorem is a comparison relating the integral closure of powers of an ideal with its ordinary power. The theorem was originally proved via analytic methods for coordinate rings of smooth varieties over the complex numbers. The full algebraic version for all regular local rings was obtained by Lipman--Sathaye. Since then, there have been other proofs and various generalizations to singularities. In this talk, we present a general Briançon-Skoda containment for pseudo-rational singularities in all characteristics. Our proof is quite simple, and it recovers most previously known results. We also prove a conjecture of Huneke on the uniform Briançon-Skoda theorem for all excellent reduced rings as an application of our results and methods. This is based on joint work with Peter McDonald, Rebecca R.G., and Karl Schwede.
By Eric Fusy
By Eric Fusy
By Charlotte Hardouin
