On the Hartshorne–Speiser–Lyubeznik theorem about Artinian modules with a Frobenius action

Sharp, Rodney

doi:10.1090/S0002-9939-06-08606-0

On the Hartshorne–Speiser–Lyubeznik theorem about Artinian modules with a Frobenius action
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by Rodney Y. Sharp PDF

Proc. Amer. Math. Soc. 135 (2007), 665-670 Request permission

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 $R$.

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