## Advanced Studies in Pure Mathematics

### Standard bases and algebraic local cohomology for zero dimensional ideals

#### Abstract

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448025

Digital Object Identifier
doi:10.2969/aspm/05610341

Mathematical Reviews number (MathSciNet)
MR2604090

Zentralblatt MATH identifier
1194.13020

#### Citation

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