Katz's theorem

Katz's theorem involves a mathematical relationship in the context of algebraic structures known as rings and modules, specifically addressing how certain algebraic objects behave under the application of a Frobenius map (a special kind of transformation). It states that, under particular conditions, the action of the Frobenius map on these modules stabilizes in a predictable way, allowing mathematicians to understand their structure and properties more clearly. Essentially, it provides insight into the deep connection between the algebraic properties of structures in characteristic p (a prime number) and how they evolve under the Frobenius transformation.