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Quasi-isomorphisms of Koszul complexes

Author: José J. M. Soto
Journal: Proc. Amer. Math. Soc. 128 (2000), 713-715
MSC (1991): Primary 13H10, 13D03
Published electronically: March 3, 1999
MathSciNet review: 1626482
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $f:A\to B$ be a surjective homomorphism of noetherian local commutative rings that induces an isomorphism between the first Koszul homology modules and an epimorphism between the second Koszul homology modules. Then $f$ induces isomorphisms between Koszul homology modules in all dimensions.

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Additional Information

José J. M. Soto
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain

Keywords: Koszul homology, regular sequence, complete intersection
Received by editor(s): February 10, 1997
Received by editor(s) in revised form: May 5, 1998
Published electronically: March 3, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society