On the Hartshorne--Speiser--Lyubeznik Theorem about Artinian modules with a Frobenius action

Abstract

Let $R$ be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring $R[x,f]$ (associated to $R$ and the Frobenius homomorphism $f$, in the indeterminate $x$) that is both $x$-torsion and Artinian over $R$.