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arXiv · 1409.2319

Graded annihilators and uniformly $F$-compatible ideals

Rodney Y. Sharp
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Abstract

Let $R$ be a commutative (Noetherian) local ring of prime characteristic $p$ that is $F$-pure. This paper is concerned with comparison of three finite sets of radical ideals of $R$, one of which is only defined in the case when $R$ is $F$-finite (that is, is finitely generated when viewed as a module over itself via the Frobenius homomorphism). Two of the afore-mentioned three sets have links to tight closure, via test ideals. Among the aims of the paper are a proof that two of the sets are equal, and a proposal for a generalization of I. M. Aberbach's and F. Enescu's splitting prime.

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Rodney Y. Sharp. 2014-09-08. Graded annihilators and uniformly $F$-compatible ideals. https://arxiv.org/abs/1409.2319

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