Y. André - Perfectoid Cohen-Macaulay rings and homological aspects of commutative algebra...
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2018-06-26

Y. André - Perfectoid Cohen-Macaulay rings and homological aspects of commutative algebra in mixed characteristic

The homological turn in commutative algebra due to Auslander and Serre was pushed forward by Peskine and Szpiro with a systematic use of the Frobenius functor, which led to tight closure theory, a powerful instrument developed by Hochster and Huneke to study singularities in characteristic p. We shall report on recent advances in the mixed characteristic case, where perfectoid Cohen-Macaulay algebras play the role of absolute integral closures in characteristic p, and lead to a mixed characteristic analog of tight closure theory.