A Characteristic p Analog of Multiplier Ideals and Applications #

Abstract

We present two applications of a characteristic p analog of multiplier ideals, which is a generalization of the test ideal in the theory of tight closure. Namely, we give alternative proofs to Smith's result on base-point-freeness of adjoint bundles in characteristic p > 0 and results on uniform behavior of symbolic powers in a regular local ring due to Ein, Lazarsfeld and Smith, and Hochster and Huneke.