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

Jun 12, 2018, 2:30 PM
Centre de Conférences Marilyn et James Simons (Le Bois-Marie)

Centre de Conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Y. André (CNRS & IMJ-PRG)


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.

Presentation materials