Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences

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This paper is concerned with ideals in a commutative Noetherian ring $R$ of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of $R$ generated by regular sequences exhibit a desirable type of `uniform' behaviour. The principal technical tool used is a result, proved by R. Hartshorne and R. Speiser in the case where $R$ is local and contains its residue field which is perfect, and subsequently extended to all local rings of prime characteristic by G. Lyubeznik, about a left 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 $R$.
Accepted for publication in the Journal of Algebra

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Commutative Algebra, 13A35; 13A15; 13E05; 13H10; 16S36

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http://salesiana.dossiersoluciones.com/handle/123456789/73998

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501501
 http://arxiv.org/abs/math/0501501

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arXiv