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

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

2006-05-12

arxiv.org/abs/math/0605330v1

Mathematics

Commutative Algebra

This is to appear in the Proceedings of the American Mathematical Society

Scientific paper

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 $R$.

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