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)

 
 

 

On the finiteness of Bass numbers
of local cohomology modules


Author: Ken-ichiroh Kawasaki
Journal: Proc. Amer. Math. Soc. 124 (1996), 3275-3279
MSC (1991): Primary 14B15, 13D03, 18G15
DOI: https://doi.org/10.1090/S0002-9939-96-03399-0
MathSciNet review: 1328354
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we show that, if $I$ is an ideal of dimension 1 of an analytically irreducible local ring, then the Bass numbers of local cohomology modules with support in $V(I)$ are finite.


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

  • 1. H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8--28. MR 27:3669
  • 2. N. Bourbaki, Algèbre commutative, Chapters 1 and 2, Hermann, Paris, 1961. MR 36:146
  • 3. D. Delfino, On cofiniteness of local cohomology modules, Math. Proc. Cambridge Philos. Soc. 115 (1994), 421--429. MR 94m:13023
  • 4. A. Grothendieck, Local cohomology, noted by R. Hartshorne, Lecture Notes in Math., vol. 41, Springer-Verlag, Berlin and New York, 1967. MR 37:219
  • 5. ------, Cohomologie locale des faisceaux cohérents et Théorèmes de Lefschtz locaux et globaux (SGA2), North-Holland, Amsterdam, 1968. MR 57:16294
  • 6. R. Hartshorne, Affine duality and cofiniteness, Invent. Math. 9 (1970), 145--164. MR 41:1750
  • 7. ------, Cohomological dimension of algebraic varieties, Ann. of Math. 88 (1968), 403--450. MR 38:1103
  • 8. ------, Algebraic geometry, Graduate Texts in Math., vol. 52, Springer-Verlag, Berlin and New York, 1977. MR 57:3116
  • 9. C. Huneke and J. Koh, Cofiniteness and vanishing of local cohomology modules, Math. Proc. Cambridge Philos. Soc. 110 (1991), 421--429. MR 92g:13021
  • 10. C. Huneke and R. Y. Sharp, Bass numbers of local cohomology module, Trans. Amer. Math. Soc. 339 (1993), 765--779. MR 93m:13008
  • 11. C. Huneke, Problems on Local Cohomology, in ``Free Resolutions in Commutative Algebra and Algebraic Geometry'', Research Notes In Math., ed. by D. Eisenbud and C. Huneke, (1992), 93--108. MR 93f:13010
  • 12. G. Lyubeznik, Finiteness properties of local cohomology modules (an application of $D$-modules to commutative algebra), Invent. Math. 113 (1993), 41--55. MR 94e:13032
  • 13. I. G. Macdonald and R. Y. Sharp, An elementary proof of the non-vanishing of certain local cohomology modules, Quart. J. Math. Oxford (2), 23 (1972), 197--204. MR 45:8646
  • 14. E. Matlis, Injective modules over noetherian rings, Pacific J. Math., 8 (1958), 511--552. MR 20:5800
  • 15. H. Matsumura, Commutative Algebra, Benjamin/Cummings, Reading, MA, 2nd ed., 1980. MR 82i:13003
  • 16. ------, Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. MR 88h:13001
  • 17. A. Ogus, Local cohomological dimension of algebraic varieties, Ann. of Math. 98 (1973), 1--34. MR 48:3964
  • 18. J. Strooker, Homological questions in local algebra, London Math. Soc. Lecture Note Ser., vol. 145, Cambridge Univ. Press, Cambridge, 1990. MR 91m:13013
  • 19. O. Zariski and P. Samuel, Commutative Algebra Vol. II, Grad. Texts in Math., vol. 29, Springer-Verlag, Berlin and New York, 1960. MR 52:10706

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14B15, 13D03, 18G15

Retrieve articles in all journals with MSC (1991): 14B15, 13D03, 18G15


Additional Information

Ken-ichiroh Kawasaki
Affiliation: Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-50, Japan
Email: kawaken@cfi.waseda.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-96-03399-0
Keywords: Local cohomology, cofinite, Bass number, analytically irreducible, Ext
Received by editor(s): February 15, 1995
Received by editor(s) in revised form: April 13, 1995
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society