Complete local factorial rings which are not Cohen-Macaulay in characteristic p

Robert M. Fossum; Phillip A. Griffith

Annales scientifiques de l'École Normale Supérieure (1975)

  • Volume: 8, Issue: 2, page 189-199
  • ISSN: 0012-9593

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Fossum, Robert M., and Griffith, Phillip A.. "Complete local factorial rings which are not Cohen-Macaulay in characteristic $p$." Annales scientifiques de l'École Normale Supérieure 8.2 (1975): 189-199. <http://eudml.org/doc/81954>.

@article{Fossum1975,
author = {Fossum, Robert M., Griffith, Phillip A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {2},
pages = {189-199},
publisher = {Elsevier},
title = {Complete local factorial rings which are not Cohen-Macaulay in characteristic $p$},
url = {http://eudml.org/doc/81954},
volume = {8},
year = {1975},
}

TY - JOUR
AU - Fossum, Robert M.
AU - Griffith, Phillip A.
TI - Complete local factorial rings which are not Cohen-Macaulay in characteristic $p$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1975
PB - Elsevier
VL - 8
IS - 2
SP - 189
EP - 199
LA - eng
UR - http://eudml.org/doc/81954
ER -

References

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  2. [B] M.-J. BERTIN, Anneaux d'invariants d'anneaux de polynômes, en caractéristique p (C. R. Acad. Sc., Paris, t. 264, série A, 1967, p. 653-656). Zbl0147.29503MR35 #6661
  3. [CE] H. CARTAN and S. EILENBERG, Homological Algebra, Princeton University Press, Princeton, 1956. Zbl0075.24305MR17,1040e
  4. [EGA] A. GROTHENDIECK et J. DIEUDONNÉ, Éléments de Géométrie algébrique (I. H. E. S. Publ. Math., vol. I n° 4, 1960; vol. IV, n° 20, 1964; vol. IV, n° 24, 1965; vol. IV, n° 28, 1966; vol. IV, n° 32, 1967). 
  5. [F] J. FOGARTY, Invariant Theory, New York-Amsterdam, Benjamin, 1969. Zbl0191.51701MR39 #1458
  6. [Fo] R. FOSSUM, The Divisor Class Group of a Krull Domain, (Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 74, Berlin-Heidelberg-New York, Springer, 1973). Zbl0256.13001MR52 #3139
  7. [FG] R. FOSSUM and P. GRIFFITH, A Complete Local Factorial Ring of Dimension 4 which is not Cohen-Macaulay (Bull. Amer. Math. Soc., vol. 81, 1975, p. 111-113). Zbl0301.13006MR50 #9858
  8. [FK] E. FREITAG und K. REINHARDT, Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen (Inventiones Math., vol. 24, 1974, p. 121-148). Zbl0304.32018MR50 #324
  9. [HO] HARTSHORNE, ROBIN and A. OGUS, On the factoriality of local rings of small embedding codimension (Comm. Alg., vol. 1, 1974, p. 415-437). Zbl0286.13013MR50 #322
  10. [H 1] M. HOCHSTER, Cohen-Macaulay Modules. In Conference on Commutative Algebra (Lecture Notes in Math., No. 311, Berlin-Heidelberg-New York, Springer, 1973). Zbl0254.13030MR49 #5006
  11. [H 2] M. HOCHSTER, Properties of Noetherian Rings Stable under General Grade Reduction (Archiv der Mathematik, vol. 24, 1973, p. 393-396). Zbl0268.13013MR48 #8485
  12. [HR] M. HOCHSTER and J. ROBERTS, Rings of Invariants of Reductive Groups Acting on Regular Rings are Cohen-Macaulay (Advances in Math., vol. 13, 1974, p. 115-175). Zbl0289.14010MR50 #311
  13. [L] J. LIPMAN, Unique Factorization in Complete Local Rings [Proceedings, 1974, Summer Institute on Algebraic Geometry, Arcata, California (to appear)]. Zbl0306.13005
  14. [M] M. PAVAMAN MURTHY, A note on factorial rings. (Archiv der Math., vol. 15, 1964, p. 418-429). Zbl0123.03401MR30 #3905
  15. [Sa] P. SAMUEL, On Unique Factorization Domains (Ill. J. Math., vol. 5, 1961, p. 1-17). Zbl0147.29202MR22 #12121
  16. [SaL] P. SAMUEL, Classes de diviseurs et dérivées logarithmiques (Topology, vol. 3, Suppl. 1, 1964, p. 81-96). Zbl0127.26002MR29 #3490
  17. [Se] J.-P. SERRE, Sur la topologie des variétés algébriques en caractéristique p (International Symposium on Algebraic Topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958). Zbl0098.13103MR20 #4559
  18. [Y] SH. YUAN, Reflexive Modules and Algebra Class Groups over Noetherian Integrally Closed Domains (J. Algebra, vol. 32, 1974, p. 405-417). Zbl0297.13010MR50 #9931

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