Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Sep 11, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Karl Schwede
Penn State
Title |
A generic restriction theorem for test ideals |
Abstract |
Suppose that f : X \to S is a flat family over a smooth variety of characteristic p > 0. In the same setting in characteristic zero, the multiplier ideal of X restricts to the multipier ideal of the fibers for most fibers X_s. There is no hope that the same statement can hold in characteristic p > 0 (either for multiplier ideals, or their analogs test ideals) because it might happen that even if X is smooth, the fibers of f might not even be reduced, and even if they are reduced, might have horrendus singularities. In this talk I will discuss a way to correct for this phenomenon, and thus obtain a generic restriction theorem for test ideals in positive characteristic. This is joint work with Zsolt Patakfalvi and Wenliang Zhang. |
Algebraic Geometry