Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology

Annals of Mathematics

Volumn 150, Issue 2, 1999, Pages 455-487

  Avramov, Luchezar L ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235422     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121087     Document Type: Article

References (46)

1. M. ANDRÉ, Méthode Simpliciale en Algèbre Homologique et Algèbre Commutative, Lecture Notes in Math. 32, Springer-Verlag, New York, 1967.
2. _, L'algèbre de Lie d'un anneau local, in Sympos. Math. (Rome, 1968/69) 4, Academic Press, London, 1970, 337-375.
3. _, Homologie des Algèbres Commutatives, Grundlehren Math. Wiss. 206, Springer-Verlag, New York, 1974.
4. _, La (2p+1)-ème déviation d'un anneau local, Enseign. Math. 24 (1977), 239-248.
5. M. AUSLANDER and D. A. BUCHSBAUM, Homological dimension in noetherian rings. II, Trans. A.M.S. 88 (1958), 194-206.
6. L. L. AVRAMOV, Flat morphisms of complete intersections, Dokl. Akad. Nauk. SSSR 225 (1975), 11-14 (Russian); Soviet Math. Dokl. 16 (1975), 1413-1417.
7. L. L. AVRAMOV, Flat morphisms of complete intersections, Dokl. Akad. Nauk. SSSR 225 (1975), 11-14 (Russian); Soviet Math. Dokl. 16 (1975), 1413-1417.
8. _, Descente des déviations par homomorphismes locaux et génération des idéaux de dimension projective finie, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 665-668.
9. _, Local algebra and rational homotopy, in Homotopie Algébrique et Algèbre Locale (Luminy, 1982), Astérisque 113-114,
10. Soc. Math. France, Paris, 1984, 15-43.
11. _, Local rings of finite simplicial dimension, Bull. A.M.S. 10 (1984), 289-291.
12. _, Infinite free resolutions, in Six Lectures on Commutative Algebra (Bellaterra, 1996), Progr. Math. 166, Birkhäuser, Basel 1998, 1-118.
13. L. L. AVRAMOV and H.-B. FOXBY, Locally Gorenstein homomorphisms, Amer. J. Math. 114 (1992), 1007-1047.
14. _, Grothendieck's localization problem, in Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, Contemp. Math. 159, A.M.S., Providence, RI, 1994, 1-13.
15. L. L. AVRAMOV and H.-B. FOXBY, Cohen-Macaulay properties of ring homomorphisms, Adv. Math. 133 (1998), 54-95.
16. L. L. AVRAMOV, H.-B. FOXBY, and B. HERZOG, Structure of local homomorphisms, J. Algebra 164 (1994), 124-145.
17. L. L. AVRAMOV and S. HALPERIN, Through the looking glass: A dictionary between rational homotopy theory and local algebra, in Algebra, Algebraic Topology, and their Interactions, (Stockholm, 1983), Lecture Notes in Math. 1183, Springer-Verlag, New York, 1986, 1-27.
18. _, On the nonvanishing of cotangent cohomology, Comment. Math. Helv. 62 (1987), 169-184.
19. A. BLANCO, J. MAJADAS, and A. G. RODICIO, Projective exterior Koszul homology and decomposition of the Tor functor, Invent. Math. 123 (1996), 123-140.
20. H. CARTAN, Algèbres d'Eilenberg-MacLane et homotopie, Séminaire H. Cartan, École Norm. Sup. (1954-55), Secrétariat Math., Paris, 1956, Exposés 3-11; Reprinted in (Euvres III, Springer-Verlag, New York, 1979, 1309-1394.
21. H. CARTAN, Algèbres d'Eilenberg-MacLane et homotopie, Séminaire H. Cartan, École Norm. Sup. (1954-55), Secrétariat Math., Paris, 1956, Exposés 3-11; Reprinted in (Euvres III, Springer-Verlag, New York, 1979, 1309-1394.
22. A. DOLD, Homology of symmetric products and other functors of complexes, Ann. of Math. 68 (1958), 54-80.
23. A. DOLD and D. PUPPE, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier Grenoble 11 (1961), 201-312.
24. A. DOLD and R. THOM, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. 67 (1958), 239-281.
25. Y. FÉLIX and S. HALPERIN, Rational LS category and its applications, Trans. A.M.S. 273 (1982), 1-38.
26. Y. FÉLIX, S. HALPERIN, and J.-C. THOMAS, The homotopy Lie algebra for finite complexes, I.H.E.S. Publ. Math. 56 (1982), 387-410.
27. W. FULTON, Intersection Theory, Ergeb. Math. Grenzgeb. 2, Springer-Verlag, New York, 1984.
28. 2-Algebras, Astérisque 186, Soc. Math. France, Paris, 1990.
29. A. GROTHENDIECK, Éléments de Géometrie Algébrique. IV (Première partie), I.H.E.S. Publ. Math. 20 (1964).
30. V. K. A. M. GUGENHEIM and J. P. MAY, On the Theory and Applications of Differential Torsion Products, Mem. A.M.S. 142, A.M.S., Providence, RI, 1974.
31. T. H. GULLIKSEN, A homological characterization of local complete intersections, Compositio Math. 23 (1971), 252-255.
32. T. H. GULLIKSEN and G. LEVIN, Homology of Local Rings, Queen's Papers Pure Appl. Math. 20, Queen's Univ., Kingston, ON, 1969.
33. S. HALPERIN, The nonvanishing of the deviations of a local ring, Comment. Math. Helv. 62 (1987), 646-653.
34. L. ILLUSIE, Complexe Cotangent et Déformations. I, Lecture Notes in Math. 239, Springer-Verlag, New York, 1971.
35. S. LICHTENBAUM and M. SCHLESSINGER, The cotangent complex of a morphism, Trans. A.M.S. 128 (1967), 41-70.
36. J. MAROT, P-rings and P-homomorphisms, J. Algebra 87 (1984), 136-149.
37. J. C. MOORE, Algèbre homologique et homologie des espaces classifiants, Séminaire H. Cartan, École Norm. Sup. (1959-60), Secrétariat Math., Paris (1961), Exposé 7.
38. M.-A. NICOLLERAT, Homology of symmetric algebras, Comm. Algebra 7 (1978), 657-676.
39. D. QUILLEN, Homotopical Algebra, Lecture Notes in Math. 43, Springer-Verlag, New York, 1967.
40. _, On the (co-)homology of commutative rings, in Applications of Categorical Algebra (New York, 1968), Proc. Sympos. Pure Math. 17, A.M.S., Providence, RI, 1970, 65-87.
41. A. RODICIO, On a result of Avramov, Manuscr. Math. 62 (1988), 181-185.
42. J.-P. SERRE, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198-232.
43. M. TABAÂ, Sur les homomorphismes d'intersection complète, C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), 437-439.
44. J. TATE, Homology of Noetherian rings and of local rings, Illinois J. Math. 1 (1957), 14-27.
45. Y. UMEDA, A remark on a theorem of J.-P. Serre, Proc. Japan. Acad. 35 (1959), 563-566.
46. K. WOLFFHARDT, Die Betti-Reihe und die Abweichungen eines lokalen Rings, Math. Z. 114 (1970), 66-78.