Mathematische Zeitschrift

, Volume 254, Issue 3, pp 627–640 | Cite as

On some local cohomology invariants of local rings

Article

Abstract

Let A be a commutative Noetherian local ring containing a field of characteristic p>0. The integer invariants λ i,j (A) have been introduced in an old paper of ours. In this paper we completely describe λ d,d (A) where d=dimA in terms of the topology of SpecA.

Keywords

Exact Sequence Spectral Sequence Local Ring Maximal Ideal Stable Part 
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References

  1. 1.
    Blickle, M., Bondu, R.: Local cohomology multiplicities in positive characteristic. preprint, 2004Google Scholar
  2. 2.
    Garcia Lopez, R., Sabbah, C.: Topological computation of local cohomology multiplicities. Dedicated to the memory of Fernando Serrano. Collect. Math. 49, 317–324 (1998)MATHGoogle Scholar
  3. 3.
    Grothendieck, A.: Local cohomology, Lecture Notes in Mathematics, v. 41, Springer, Heidelberg, 1967Google Scholar
  4. 4.
    Hartshorne, R.: Complete intersections and connectedness. Amer. J. Math. 84, 497–508 (1962)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Hartshorne, R.: Cohomological Dimension of Algebraic Varieties. Ann. Math. 88, 403–450 (1968)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Hochster, M., Huneke, C.: Indecomposable canonical modules and connectedness. Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), 197–208, Contemp. Math. 159, Amer. Math. Soc. Providence, RI, 1994Google Scholar
  7. 7.
    Huneke, C., Lyubeznik, G.: On the vanishing of local cohomology modules. Invent. Math. 102, 73–93 (1990)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Kawasaki, K.-I., On the Lyubeznik number of local cohomology modules. Bull. Nara Univ. Ed. Natur. Sci. 49 5–7 (2000)Google Scholar
  9. 9.
    Kawasaki, K.-I.: On the highest Lyubeznik number. Math. Proc. Cambr. Phil. Soc. 132, no. 3, 409–417 (2002)Google Scholar
  10. 10.
    Lyubeznik, G.: Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra). Invent. Math. 113, 41–55 (1993)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Lyubeznik, G.: F-modules: applications to local cohomology and D-modules in characteristic p>0. J. reine angew. Math. 491, 65–130 (1997)MATHMathSciNetGoogle Scholar
  12. 12.
    Lyubeznik, G.: A partial survey of local cohomology. Local cohomology and its applications (Guanajuato, 1999), 121–154, Lecture Notes in Pure and Appl. Math., 226, Marcel Dekker, Inc., New York, 2002Google Scholar
  13. 13.
    Ogus, A.: Local Cohomological Dimension of Algebraic Varieties. Ann. Math. 98, 327–365 (1973)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Peskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. Applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck. Inst. Hautes Études Sci. Publ. Math. 42, 47–119 (1973)MathSciNetGoogle Scholar
  15. 15.
    Walther, U.: On the Lyubeznik numbers of a local ring. Proceedings of the AMS, 129(6), 1631–1634 (2001)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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