Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

A counterexample to the rigidity conjecture for rings


Author: Raymond C. Heitmann
Journal: Bull. Amer. Math. Soc. 29 (1993), 94-97
MSC (2000): Primary 13D05; Secondary 18G15
DOI: https://doi.org/10.1090/S0273-0979-1993-00410-5
MathSciNet review: 1197425
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.


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

  • [1] M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631-645. MR 0179211 (31:3460)
  • [2] W. Bruns, Divisors on varieties of complexes, Math. Ann. 264 (1983), 53-71. MR 709861 (85d:13021)
  • [3] S. Dutta, M. Hochster, and J. McLaughlin, Modules of finite projective dimension with negative intersection multiplicities, Invent. Math. 79 (1985), 253-291. MR 778127 (86h:13023)
  • [4] M. Hochster, Topics in the homological theory of modules over commutative rings, CBMS Regional Conf. Ser. in Math., vol. 24, Amer. Math. Soc., Providence, RI, 1975. MR 0371879 (51:8096)
  • [5] S. Lichtenbaum, On the vanishing of Tor in regular local rings, Illinois J. Math. 10 (1966), 220-226. MR 0188249 (32:5688)
  • [6] C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Inst. Hautes Études Sci. Publ. Math. 42 (1973), 47-119. MR 0374130 (51:10330)
  • [7] P. Roberts, The vanishing of intersection multiplicities of perfect complexes, Bull. Amer. Math. Soc. 13 (1985), 127-130. MR 799793 (87c:13030)
  • [8] -, Intersection theorems, Commutative Algebra, Math. Sci. Res. Inst. Publ., vol. 15, Springer-Verlag, New York, 1989, pp. 417-436. MR 1015532 (90j:13024)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 13D05, 18G15

Retrieve articles in all journals with MSC (2000): 13D05, 18G15


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1993-00410-5
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society