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On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action |
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| Authors: | Rodney Y. Sharp |
| Affiliation: | Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom |
| Abstract: | Let  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]$](http://www.ams.org/proc/2007-135-03/S0002-9939-06-08606-0/gif-abstract0/img2.gif){kind=small} (associated to  and the Frobenius homomorphism  , in the indeterminate  ) that is both  -torsion and Artinian over  . |
| Keywords: | Commutative Noetherian ring prime characteristic Frobenius homomorphism Artinian module Frobenius skew polynomial ring |
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