Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Grothendieck groups for hypersurface rings


Author: Øyvind Solberg
Journal: Proc. Amer. Math. Soc. 109 (1990), 943-950
MSC: Primary 13D15; Secondary 16A54, 18F30, 19A31
DOI: https://doi.org/10.1090/S0002-9939-1990-1027101-5
MathSciNet review: 1027101
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ and $ S$ be commutative complete noetherian local Gorenstein domains. If the category of finitely generated maximal Cohen-Macaulay modules over $ R$ and $ S$ are stably equivalent and the equivalence commutes with the first syzygy functors, then we show that the Grothendieck groups for $ R$ and $ S$ are isomorphic. In particular, we apply this result to hypersurface rings.


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

  • [1] M. Auslander, Functors and morphisms determined by objects, Proc. Conf. Representation Theory (Philadelphia, 1976), Marcel Dekker, New York, 1978, pp. 1-244. MR 0480688 (58:844)
  • [2] -, Isolated singularities and existence of almost split sequences, Representation Theory II, Lecture Notes in Math., vol. 1178, Springer-Verlag, New York, 1986, pp. 194-241. MR 842486 (87j:13029)
  • [3] M. Auslander and I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39 (1986), 1-51. MR 816889 (87g:16038)
  • [4] -, Representation theory of artin algebras VI: A functorial approach to almost split sequences, Comm. Algebra 11 (1977), 257-300. MR 0472919 (57:12601)
  • [5] -, Stable equivalence of artin algebras, Proc. Conf. on Orders, Group Rings and Related Topics, Lecture Notes in Math., vol. 353, Springer-Verlag, 1972, pp. 8-71. MR 0335575 (49:356)
  • [6] J. Herzog and H. Sanders, The Grothendieck groups of invariant rings and of simple hypersurface singularities, Proc. of Conf. on Singularities, Representation of Algebras and Vector Bundles, Lecture Notes in Math., vol. 1273, Springer-Verlag, 1987, pp. 134-149. MR 915171 (89b:14004)
  • [7] R.-O. Buchweitz, G.-M. Greuel, and F. O. Shreyer, Cohen-Macaulay modules on hypersurface singularities. II, Invent. Math. 88 (1987), 165-182. MR 877011 (88d:14005)
  • [8] H. Knörrer, Cohen-Macaulay modules on hypersurface singularities. I, Invent. Math. 88 (1987), 153-164. MR 877010 (88d:14004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13D15, 16A54, 18F30, 19A31

Retrieve articles in all journals with MSC: 13D15, 16A54, 18F30, 19A31


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1027101-5
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society