André-Quillen homology of algebra retracts
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 3, pp. 431-462. 
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     author = {Avramov, Luchezar L. and Iyengar, Srikanth},
     title = {Andr\'e-Quillen homology of algebra retracts},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {431--462},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
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     year = {2003},
     doi = {10.1016/S0012-9593(03)00014-4},
     zbl = {1079.13503},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0012-9593(03)00014-4/}
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Avramov, Luchezar L.; Iyengar, Srikanth. André-Quillen homology of algebra retracts. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 3, pp. 431-462. doi : 10.1016/S0012-9593(03)00014-4. http://archive.numdam.org/articles/10.1016/S0012-9593(03)00014-4/

[1] André M., Méthode simpliciale en algèbre homologique et algèbre commutative, Lecture Notes Math., 32, Springer-Verlag, Berlin, 1967. | MR | Zbl

[2] André M., Homologie des algèbres commutatives, Grundlehren Math. Wiss., 206, Springer-Verlag, Berlin, 1974. | MR | Zbl

[3] André M., Algèbres graduées associées et algèbres symétriques plates, Comment. Math. Helv. 49 (1974) 277-301. | MR | Zbl

[4] André M., Localisation de la lissité formelle, Manuscripta Math. 13 (1974) 297-307. | MR | Zbl

[5] André M., Algèbre homologique des anneaux locaux à corps résiduels de caractéristique deux, in: Sém. d'Algèbre P. Dubreil (Paris, 1979), Lecture Notes Math., 740, Springer-Verlag, Berlin, 1979, pp. 237-242. | MR | Zbl

[6] André M., Le caractère additif des déviations des anneaux locaux, Comment. Math. Helv. 57 (1982) 648-675. | MR | Zbl

[7] Avramov L.L., Homology of local flat extensions and complete intersection defects, Math. Ann. 228 (1977) 27-37. | MR | Zbl

[8] Avramov L.L., Small homomorphisms of local rings, J. Algebra 50 (1978) 400-453. | MR | Zbl

[9] Avramov L.L., Infinite free resolutions, in: Six Lectures in Commutative Algebra (Bellaterra, 1996), Progress in Math., 166, Birkhäuser, Boston, 1998, pp. 1-118. | MR | Zbl

[10] Avramov L.L., Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology, Ann. of Math. (2) 150 (1999) 455-487. | MR | Zbl

[11] Avramov L.L., Foxby H.-B., Herzog B., Structure of local homomorphisms, J. Algebra 164 (1994) 124-145. | MR | Zbl

[12] Avramov L.L., Halperin S., Through the looking glass: A dictionary between rational homotopy theory and local algebra, in: Algebra, Algebraic Topology, and Their Interactions (Stockholm, 1983), Lecture Notes Math., 1183, Springer-Verlag, Berlin, 1986, pp. 1-27. | MR | Zbl

[13] Avramov L.L., Iyengar S., Finite generation of Hochschild homology algebras, Invent. Math. 140 (2000) 143-170. | MR | Zbl

[14] Avramov L.L., Iyengar S., Homological criteria for regular homomorphisms and for locally complete intersection homomorphisms, in: Algebra, Arithmetic and Geometry (Mumbay, 2000), T.I.F.R. Studies in Math. 16, I, Narosa, New Delhi, 2002, pp. 97-122. | MR | Zbl

[15] Cartan H., Algèbres d'Eilenberg-MacLane, Exposés 2 à 11, Sém. H. Cartan, Éc. Normale Sup. (1954-1955), Secrétariat Math., Paris, 1956; reprinted in: Œuvres, Vol. III, Springer-Verlag, Berlin, 1979, pp. 1309-1394.

[16] Cartan H., Eilenberg S., Homological Algebra, Princeton Univ. Press, Princeton, NJ, 1956. | MR | Zbl

[17] Félix Y., Halperin S., Rational L.-S. category and its applications, Trans. Amer. Math. Soc. 273 (1982) 1-37. | MR | Zbl

[18] Gulliksen T.H., A proof of the existence of minimal algebra resolutions, Acta Math. 120 (1968) 53-58. | MR | Zbl

[19] Gulliksen T.H., Levin G., Homology of local rings, Queen's Papers Pure Appl. Math., Queen's Univ., Kingston, Ont. 20 (1969). | MR | Zbl

[20] Hochschild G., Kostant B., Rosenberg A., Differential forms on a regular affine algebra, Trans. Amer. Math. Soc. 102 (1962) 383-408. | MR | Zbl

[21] Iyengar S., Acyclicity of Tate constructions, J. Pure Appl. Algebra 163 (2001) 289-300. | MR | Zbl

[22] Levin G., Homology of local rings, Ph.D. Thesis, Univ. of Chicago, Chicago, IL, 1965.

[23] Levin G., Large homomorphisms of local rings, Math. Scand. 46 (1980) 209-215. | MR | Zbl

[24] Maclane S., Homology, Grundlehren Math. Wiss., 114, Springer-Verlag, Berlin, 1967. | MR | Zbl

[25] Quillen D., On the (co-)homology of commutative rings, in: Applications of Categorical Algebra (New York, 1968), Proc. Symp. Pure Math., 17, American Mathematical Society, Providence, RI, 1970, pp. 65-87. | MR | Zbl

[26] Schoeller C., Homologie des anneaux locaux noethériens, C. R. Acad. Sci. Paris Sér. A 265 (1967) 768-771. | MR | Zbl

[27] Şega L.M., Homological properties of powers of the maximal ideal of a local ring, J. Algebra 241 (2001) 827-858. | MR | Zbl

[28] Turner J., Nilpotency in the homotopy of simplicial commutative algebras, Preprint, 2001.

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