Time: 14:00 pm, Tuesday, 27/04/2021

Venue: Room 302, A5, Institute of Mathematics, VAST

Abstract: Let R--->A be a morphism of commutative rings, where R is noetherian, and M is an A-module. We discuss a fiber criterion to check the flatness of M as an R-module. This criterion can be used to test the faithful flatness and purity of module maps. The motivation for our work is some result of the type "injectivity implies faithful flatness", about morphisms between affine group schemes over a base field. We also discuss some intriguing questions on fiber flatness criteria.