Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 341 - 361
Standard bases and algebraic local cohomology for zero dimensional ideals
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.
Received: 13 April 2008
Revised: 11 July 2008
First available in Project Euclid: 28 November 2018
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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. https://projecteuclid.org/euclid.aspm/1543448025