49:50
published on March 27, 2026
Generalized binomial edge ideals are Cartwright-Sturmfels
By Emanuela De Negri
The Briançon-Skoda theorem revisited
By Linquan Ma
Appears in collection : The Ubiquity of Commutative Algebra / Ubiquité de l'algèbre commutative
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.
