Cohen-Macaulay Properties of Ring Homomorphisms

Advances in Mathematics

Volumn 133, Issue 1, 1998, Pages 54-95

  Avramov, Luchezar L ^a   Foxby, Hans Bjørn ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002867256     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1997.1684     Document Type: Article

References (36)

1. Avramov L. L., Foxby H.-B. Gorenstein local homomorphisms. Bull. Amer. Math. Soc. (N.S.). 23:1990;145-150.
2. Avramov L. L., Foxby H.-B. Homological dimensions of unbounded complexes. J. Pure Appl. Algebra. 71:1991;129-155.
3. Avramov L. L., Foxby H.-B. Locally Gorenstein homomorphisms. Amer. J. Math. 114:1992;1007-1047.
4. L. L. Avramov, H.-B. Foxby, Grothendieck's localization problem, Syzygies, Multiplicities, and Birational Algebra, Contemporary Mathematics, 159, 1, 13, Amer. Math. Soc. Providence, RI.
5. Avramov L. L., Foxby H.-B., Halperin J. S. Descent and ascent of local properties along homomorphisms of finite flat dimension. J. Pure Appl. Algebra. 38:1986;167-185.
6. Avramov L. L., Foxby H.-B., Herzog B. Structure of local homomorphisms. J. Algebra. 146:1994;124-145.
7. Avramov L. L., Foxby H.-B., Lescot J. Séries de Bass des homomorphismes locaux de Tor-dimension finie. C. R. Acad. Sci. Paris Sér. I. 309:1989;645-649.
8. Avramov L. L., Foxby H.-B., Lescot J. Bass series of local ring homomorphisms of finite flat dimension. Trans. Amer. Math. Soc. 335:1993;497-523.
9. Bruns W., Vetter U. Determinantal Rings. Lecture Notes in Math. 1327:1988;Springer-Verlag, Berlin/Heidelberg/New York.
10. Ferrand D., Raynaud M. Fibres formelles d'un anneau local noethérien. Ann. Sci. École Norm. Supér. (4). 3:1970;293-311.
11. Foxby H.-B. Bounded complexes of flat modules. J. Pure Appl. Algebra. 5:1979;149-172.
12. Foxby H.-B. Preprint Series. 1981.
13. Foxby H.-B., Thorup A. Minimal injective resolutions under flat base change. Proc. Amer. Math. Soc. 67:1977;27-31.
14. Gel'fand S. I., Manin Yu I. Methods of Homological Algebra. I. Introduction to Cohomology Theory and Derived Categories. 1988;Nauka, Moscow.
15. Grivel P.-P. Catégories dérivées et foncteurs dérivés. Borel A. AlgebraicD. Perspectives in Math. 2:1987;1-108 Academic Press, Boston/Orlando/San Diego.
16. Grothendieck A. Éléments de géométrie algébrique, IV. Étude local des schémas et des morphismes de schémas. Inst. Hautes Études Sci. Publ. Math. 20, 24, 28, 32:1964-1967.
17. Hartshorne R. Residues and Duality. Lecture Notes in Math. 20:1971;Springer-Verlag, Berlin/Heidelberg/New York.
18. Herzog J., Kunz E. Der kanonische Modul eines Cohen-Macaulay Rings. Lecture Notes in Math. 238:1971;Springer-Verlag, Berlin/Heidelberg/New York.
19. Hochster M. Topics in the Homological Theory of Modules over Commutative Rings. CBMS Regional Conference Series in Math. 24:1975;Amer. Math. Soc. Providence.
20. Hochster M. Canonical elements in local cohomology modules and the direct summand conjecture. J. Algebra. 84:1983;503-553.
21. Iversen B. Amplitude inequalities for complexes. Ann. Sci. École Norm. Supér. (4). 10:1977;547-558.
22. Matsumura H. Commutative Algebra. 1980;Benjamin/Cummings, Reading.
23. Matsumura H. Commutative Ring Theory. Cambridge Studies in Advanced Math. 8:1986;Cambridge Univ. Press, Cambridge.
24. McAdam S., Ratliff L. J. Jr. Semi-local taut rings. Indiana Univ. Math. J. 26:1977;73-79.
25. Ogoma T. Non-catenary pseudo-geometric local rings. Jpn. J. Math. 6:1980;147-163.
26. Peskine C., Szpiro L. Sur la topologie des sous-schémas fermés d'un schéma localement noethérien définis comme supports d'un fasiceau cohérent localement de dimension projective finie. C. R. Acad. Sci. Paris Sér. A. 269:1969;49-51.
27. Peskine C., Szpiro L. Dimension projective finie et cohomologie locale. Inst. Hautes Études Sci. Publ. Math. 42:1973;47-119.
28. Peskine C., Szpiro L. Syzygies et multiplicités. C. R. Acad. Sci. Paris Sér. A. 278:1974;1421-1424.
29. Ratliff L. J. Jr. Catenary rings and the altitude formula. Amer. J. Math. 94:1972;458-466.
30. Roberts P. Two applications of dualizing complexes over local rings. Ann. Sci. École Norm. Supér. (4). 9:1976;103-106.
31. Roberts P. Homological Invariants of Modules over Commutative Rings. Sém. Math. Sup. 72:1980;Presses Univ. Montréal, Montréal.
32. Roberts P. Le théorème d'intersection. C. R. Acad. Sci. Paris Sér. I. 304:1987;177-180.
33. Roberts P. The homological conjectures. Eisenbud D., Huneke C. Free Resolutions in Commutative Algebra and Algebraic Geometry. Sundance 90. Research Notes in Math. 2:1992;121-132 Jones and Bartlett, Boston/London.
34. Serre J.-P. Rapport au comité Fields sur les travaux de A. Grothendieck. K. 3:1989;199-204.
35. Spaltenstein N. Resolutions of unbounded complexes. Compositio Math. 65:1988;121-154.
36. Verdier J.-L. Catégories dérivées. Quelques résultats (État 0). SGA 4 1 2 . Lecture Notes in Math. 569:1977;Springer-Verlag, Berlin/Heidelberg/New York. p. 262-311.