Multiplier Ideals and Finite Morphisms in Positive Characteristic

Abstract:  Pairs (X, D) where X is a normal algebraic variety and D an effective Q-divisor arise naturally throughout algebraic geometry.  For example, these divisors may represent the boundaries of open varieties, markings in moduli problems, or simply error terms in adjunction formulae.  Multiplier ideals are invariants used to study the subtle local structure of the singular or non-manifold points of such pairs -- a critical part of many investigations.  Although first defined analytically for pairs defined over the complex numbers, in this talk we shall recall the algebraic formulation which is valid in arbitrary characteristic.    We will go on to discuss results concerning the pathological behavior of multiplier ideals over finite surjective morphisms in positive characteristic.  Time permitting, we will discuss the relationship of the multiplier ideal to another invariant of pairs in positive characteristic called the test ideal.  This is joint work in progress with Karl Schwede.