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

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

2005-01-28

arxiv.org/abs/math/0501501v1

Mathematics

Commutative Algebra

Accepted for publication in the Journal of Algebra

Scientific paper

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 $R$.

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