Skip to main content
SpringerLink
Log in

Tight closure of parameter ideals

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [Ab] Aberbach, I.: Tight closure inF-rational rings. (Preprint)

  • [An1] André, M.: Cinq Exposés sur la desingularization. (Preprint)

  • [Ar1] Artin, M.: Algebraic approximation of structures over complete local rings. Publ. Math., Inst. Hautes Étud. Sci.36, 23–58 (1969)

    Google Scholar 

  • [Ar2] Artin, M.: On the joins of Hensel rings. Adv. Math.7, 282–296 (1971)

    Google Scholar 

  • [AHH] Aberbach, I., Hochster, M., Huneke, C.: Localization of tight closure and modules of finite phantom projective dimension. J. Reine Angew. Math.434, 67–114 (1993).

    Google Scholar 

  • [FW] Fedder, R., Watanabe, K.: A characterization of F-regularity in terms of F-Purity. In: Hochster, M. et al. (eds.) commutative algebra. (Publ., Math. Sci. Res. Inst., vol. 15, pp. 227–245) Berlin Heidelberg New York: Springer: 1989

    Google Scholar 

  • [HH1] Hochster, M., Huneke, C.: Tight closure, invariant theory and the Briançon-Skoda theorem. Am. Math. Soc.3, 31–116 (1990)

    Google Scholar 

  • [HH2] Hochster, M., Huneke, C.: Infinite integral extensions and big Cohen-Macaulay algebras. Ann. Math.135, 53–89 (1992)

    Google Scholar 

  • [HH3] Hochster, M., Huneke, C.: Tight closures of parameter ideals and splitting in module-finite extensions. J. Alg. Geom. (to appear)

  • [HH4] Hochster, M., Huneke, C.; F-regularity, test elements, and smooth base change. (Preprint)

  • [HH5] Hochster, M., Huneke, C.: Applications of the existence of big Cohen-Macaulay algebras. (Preprint)

  • [LTXX] Lipman, J., Tessier, B. Pseudo-rational local rings and a theorem of Briançon-Skoda on the integral closures of ideals. Mich. Math. J.28, 97–116 (1981)

    Google Scholar 

  • [KAP] Kaplansky, I.: Commutative Algebra. Chicago: University of Chicago Press 1974

    Google Scholar 

  • Ogoma, T.: General Néron desingularization based on the idea of Popescu. J. Algebra (to appear)

  • [PS] Peskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. Publ. Math. Inst. Hautes Étud. Sci.,42, 323–395 (1973)

    Google Scholar 

  • [P1] Popescu, D.: General Néron desingularization. Nagoya Math. J.100, 97–126 (1985)

    Google Scholar 

  • [P2] Popescu, D.: General Néron desingularization and approximation. Nagoya Math. J.104, 85–115 (1986)

    Google Scholar 

  • [S1] Smith, K.E.: F-rational rings have rational singularities. (Preprint)

  • [S2] Smith, K.E.: Test elements in local rings (in preparation)

  • [Sp] Spivakovsky, M.: Smoothing of ring homomorphisms, approximation theorems and the Bass-Quillen conjecture. (Preprint)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47906, W-LaFayette, IN, USA

    K. E. Smith

Authors
  1. K. E. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum 10-IV-1992 & 24-V-1993

The author is supported by the Alfred P. Sloan Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, K.E. Tight closure of parameter ideals. Invent Math 115, 41–60 (1994). https://doi.org/10.1007/BF01231753

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231753

Keywords

Search

Navigation