Illinois Journal of Mathematics

Test exponents for modules with finite phantom projective dimension

Melvin Hochster and Yongwei Yao

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Abstract

Let $(R,\mathfrak{m})$ be an equidimensional excellent local ring of prime characteristic $p>0$. We give an alternate proof of the existence of a uniform test exponent for any given $c\in R^{\circ}$ and all ideals generated by (full or partial) systems of parameters. This follows from a more general result about the existence of a test exponent for any given Artinian $R$-module. If we further assume $R$ is Cohen–Macaulay, then there exists a test exponent for any given $c\in R^{\circ}$ and all perfect modules with finite projective dimension.

Article information

Source
Illinois J. Math., Volume 56, Number 4 (2012), 1095-1107.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1399395824

Digital Object Identifier
doi:10.1215/ijm/1399395824

Mathematical Reviews number (MathSciNet)
MR3231475

Zentralblatt MATH identifier
1299.13008

Subjects
Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 13C13: Other special types 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Hochster, Melvin; Yao, Yongwei. Test exponents for modules with finite phantom projective dimension. Illinois J. Math. 56 (2012), no. 4, 1095--1107. doi:10.1215/ijm/1399395824. https://projecteuclid.org/euclid.ijm/1399395824


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