Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

A counterexample to the rigidity conjecture for rings

Author(s): Raymond C. Heitmann
Journal: Bull. Amer. Math. Soc. 29 (1993), 94-97.
MSC (2000): Primary 13D05; Secondary 18G15
MathSciNet review: 1197425
Retrieve article in: PDF

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:

[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: 10.1090/S0273-0979-1993-00410-5
PII: S 0273-0979(1993)00410-5
Copyright of article: Copyright 1993, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia