Advanced Studies in Pure Mathematics

A note on Bockstein homomorphisms in local cohomology

Anurag K. Singh and Uli Walther

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Abstract

This note is an exposition on the results from [SiW] related to Lyubeznik's conjecture on local cohomology. We use the method of Bockstein homomorphisms, which to our knowledge has not been employed before in commutative algebra. As an example, we strengthen the classical Stanley–Reisner correspondence by relating Bockstein homomorphisms on local cohomology in monomial rings to the topological Bockstein homomorphisms of simplicial complexes.

We introduce the necessary language in Section 1, then present the motivation with our main theorem in Section 2, and finally illustrate our results in the case of Stanley–Reisner ideals in Section 3.

Article information

Source
Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 513-521

Dates
Received: 16 April 2010
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085020

Digital Object Identifier
doi:10.2969/aspm/06210513

Mathematical Reviews number (MathSciNet)
MR2933808

Zentralblatt MATH identifier
1268.13006

Subjects
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]

Keywords
Bockstein local cohomology Lyubeznik conjecture Stanley-Reisner

Citation

Singh, Anurag K.; Walther, Uli. A note on Bockstein homomorphisms in local cohomology. Arrangements of Hyperplanes — Sapporo 2009, 513--521, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06210513. https://projecteuclid.org/euclid.aspm/1543085020


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