Advanced Studies in Pure Mathematics

Standard bases and algebraic local cohomology for zero dimensional ideals

Shinichi Tajima, Yayoi Nakamura, and Katsusuke Nabeshima

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Zero-dimensional ideals in the formal power series and the associated vector space consisting of algebraic local cohomology classes are considered in the context of Grothendieck local duality. An algorithmic strategy for computing relative Čech cohomology representations of the algebraic local cohomology classes are described. A new algorithmic method for computing standard bases of a given zero-dimensional ideal is derived by using algebraic local cohomology and the Grothendieck local duality.

Article information

Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 341-361

Received: 13 April 2008
Revised: 11 July 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document euclid.aspm/1543448025

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15] 32C37: Duality theorems 13J05: Power series rings [See also 13F25] 32A27: Local theory of residues [See also 32C30]

Standard bases algebraic local cohomology Grothendieck duality


Tajima, Shinichi; Nakamura, Yayoi; Nabeshima, Katsusuke. Standard bases and algebraic local cohomology for zero dimensional ideals. Singularities — Niigata–Toyama 2007, 341--361, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610341.

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