Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

  • 1. M. André, Homologie des Algèbres Commutatives, Springer, Berlin (1974). MR 50:4707
  • 2. E. F. Assmus, On the homology of local rings, Illinois J. Math. 3 (1959), 187-199. MR 21:2670
  • 3. L. L. Avramov, Descente des déviations par homomorphismes locaux et génération des ideaux de dimension projective finie, C. R. Acad. Sci. Paris 295 (1982), 665-668. MR 85a:14007
  • 4. L. L. Avramov and E. S. Golod, Homology algebra of the Koszul complex of a local Gorenstein ring, Math. Notes Acad. Sci. USSR 9 (1971), 30-32. MR 43:4883
  • 5. W. Bruns, On the Koszul algebra of a local ring, Illinois J. Math. 37 (1993), 278-283. MR 94c:13012
  • 6. D. Quillen, On the (co-)homology of commutative rings, Proc. Symp. Pure Math. 17 (1970), 65-87. MR 41:1722
  • 7. A. G. Rodicio, On a result of Avramov, Manuscripta Math. 62 (1988), 181-185. MR 89k:13014
  • 8. S. S. Strogalov, Quasiisomorphisms of a Koszul complex. (Russian) Uspehi Mat. Nauk 28 (1973), no. 6 (174), 196. MR 52:13822
  • 9. S. S. Strogalov, On Poincaré series, Math. USSR Izvestija 12 (1978), 391-425.
  • 10. J. Tate, Homology of noetherian rings and local rings, Illinois J. Math. 1 (1957), 14-27. MR 19:119b

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13H10, 13D03

Retrieve articles in all journals with MSC (1991): 13H10, 13D03

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

American Mathematical Society