Mon, March 19, 2018
4:00 pm - 5:00 pm
TBD
Speaker: Hans Schoutens, CUNY
Title: Tight closure from the point-of-view of difference closure
Abstract: Tight closure is a very elegant yet powerful theory developed by Hochster and Huneke in the 90s. It exploits good properties of the Frobenius (=the $p$-th power map in positive characteristic) to prove rather quickly some deep theorems in algebra and algebraic geometry. Since there is no apparent Frobenius in characteristic zero, the theory is much more cumbersome there, unless one takes the point of view of difference closures (and some 'mild’ use of ultraproducts). Rather than giving all the details, I will give a brief survey—Tight Closure 101—and then give some nice applications.