We have long known, or implicitly used, that to a potential splitting \phi of the Frobenius homomorphism on a ring R of positive characteristic one can assign a divisor on Spec(R), and these divisors describe the Frobenius splitting behavior of \phi at height one primes. We generalize this process and assign coefficients called log discrepancies to valuations on Spec(R/P) for primes P of R. Using these log discrepancies, we can characterize the Frobenius splitting behavior of \phi at any point of Spec(R). Speaker(s): Eric Canton (University of Nebraska)