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

Rodney Y. Sharp

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

Commutative Algebra 2007-05-23 v1

Authors: Rodney Y. Sharp

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 $R$ .

Keywords

commutative noetherian local ring prime characteristic frobenius action artinian module skew polynomial ring hartshorne-speiser-lyubeznik theorem

Cite

@article{arxiv.math/0605330,
  title  = {On the Hartshorne--Speiser--Lyubeznik Theorem about Artinian modules with a Frobenius action},
  author = {Rodney Y. Sharp},
  journal= {arXiv preprint arXiv:math/0605330},
  year   = {2007}
}

Comments

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

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