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.