Skip to main content
SpringerLink
Log in

Dimension projective finie et cohomologie locale

Applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck

  • Published:
Publications Mathématiques de l'Institut des Hautes Études Scientifiques Aims and scope Submit manuscript

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

Bibliographie

  1. M. Artin, Algebraic approximation of structures over complete local rings,Publ. Math. I.H.E.S.,36, 1969.

  2. M. Auslander, Modules over unramified regular local rings,Ill. J. of Math.,5 (1961), 631–645.

    MATH  MathSciNet  Google Scholar 

  3. M. Auslander, Modules over unramified regular local rings,Proc. Intern. Congress of math., 1962, 230–233.

  4. M. Auslander, On the purity of branch locus,Amer. J. of Math.,84 (1962), 116–125.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Auslander etD. Buchsbaum, Homological codimension and multiplicity,Ann. of Math.,68 (1958), 626–657.

    Article  MathSciNet  Google Scholar 

  6. H. Bass, On the ubiquity of Gorenstein rings,Math. Zeitschr.,82 (1963), 8–28.

    Article  MATH  MathSciNet  Google Scholar 

  7. N. Bourbaki,Algèbre commutative, Hermann, Paris, 1961–65.

    Google Scholar 

  8. H. Cartan etS. Eilenberg,Homological algebra, Princeton University Press, 1956.

  9. Gabriel, Objects injectifs dans les catégories abéliennes,Séminaire Dubreil-Pisot, Algèbre et théorie des nombres, 12e année, 1958–1959, no 17, 32 p.

  10. A. Grothendieck,Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), North Holland, Amsterdam, 1968.

  11. A. Grothendieck, Local cohomology,Lectures notes on mathematics, no 41, Springer Verlag, 1967.

  12. A. Grothendieck, Éléments de géométrie algébrique,Publ. Math. I.H.E.S., nos 4, 8, 11, 17, 20, 24, 32.

  13. R. Hartshorne, Residues and duality,Lectures notes on mathematics, no 20, Springer Verlag, 1966.

  14. R. Hartshorne, Cohomological dimension of algebraic varieties,Ann. of Math.,88 (1968), 403–450.

    Article  MathSciNet  Google Scholar 

  15. R. Hartshorne, Ample subvarieties of algebraic varieties,Lectures notes in mathematics, no 156, Springer Verlag, 1970.

  16. Horrocks, Vector bundles on the punctured spectrum of a local ring,Proc. Lond. Math. Soc. (3),14 (1964), 689–713.

    Article  MATH  MathSciNet  Google Scholar 

  17. S. Kleimann, On the vanishing of Hn(X,J) for ann-dimensional variety,Proc. Amer. Math. Soc.,18 (1967), 940–944.

    Article  MathSciNet  Google Scholar 

  18. E. Kunz, Characterisations of regular local rings of characteristicp, Amer. J. of Math.,41 (1969), 772–784.

    Article  MathSciNet  Google Scholar 

  19. S. Lichtenbaum, On the vanishing of Tor in regular local rings,Ill. J. of Math.,10 (1966), 220–226.

    MATH  MathSciNet  Google Scholar 

  20. Macaulay,Algebraic theory of modular systems, Cambridge tracts, no 19, 1916.

  21. D. Rees, The grade of an ideal or module,Proc. Camb. phil. soc.,53 (1957), 28–42.

    Article  MATH  MathSciNet  Google Scholar 

  22. P. Samuel,Séminaire d’algèbre commutative, Anneaux de Gorenstein et torsion en algèbre commutative. Secrétariat mathématique, 11, rue Pierre Curie, Paris (5e), 1967.

  23. J.-P. Serre, Algèbre locale et multiplicité,Lectures notes in mathematics, no 11, Springer Verlag, 1965.

  24. D. A. Buschbaum, Complexes associated with the minors of a matrix,Symposia Matematica, vol. IV, 1970, Bologna.

Download references

Authors
  1. C. Peskine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Szpiro
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Peskine, C., Szpiro, L. Dimension projective finie et cohomologie locale. Publications Mathématiques de l’Institut des Hautes Scientifiques 42, 47–119 (1973). https://doi.org/10.1007/BF02685877

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02685877

Search

Navigation