Singularities and Persistence Conditions in Prime Characteristic Commutative Algebra

This document contains results pertaining to singularities in prime characteristic commutative algebra. Chapter 1 reviews definitions of various singularities detected by the Frobenius endomorphism. The content of Chapter 2 includes base change results for F-nilpotent rings. The main result of Chapter 3 is that F-purity deforms in Q-Gorenstein rings. Chapter 4 studies the behavior of the Hilbert-Kunz multiplicity under general hyperplane sections. Chapter 5continues the study F-coherent rings.