Time: Saturday, December 3, from 2:30pm to 4:30pm (Hanoi time)

Venue: Room 301, Building A5, Institute of Mathematics

Abstract: Macaulayfications are weak variants of resolutions of singularities in which Cohen-Macaulay property replaces regularity. While resolutions of singularities have not been constructed for almost Noetherian schemes over positive characteristics, Macaulayfications exist for a large class of Noetherian schemes over any characteristic due to the works of Faltings, Kawasaki, Cesnavicius and others. In this talk, I first review briefly a history of this problem, then I give a necessary condition for existence of Macaulayfication with some applications.