@incollection{AST_1984__113-114__15_0,
author = {Avramov, Luchezar L.},
title = {Local algebra and rational homotopy},
booktitle = {Homotopie alg\'ebrique et alg\`ebre locale},
series = {Ast\'erisque},
pages = {15--43},
year = {1984},
publisher = {Soci\'et\'e math\'ematique de France},
number = {113-114},
mrnumber = {749041},
zbl = {0552.13003},
language = {en},
url = {https://www.numdam.org/item/AST_1984__113-114__15_0/}
}
TY - CHAP AU - Avramov, Luchezar L. TI - Local algebra and rational homotopy BT - Homotopie algébrique et algèbre locale AU - Collectif T3 - Astérisque PY - 1984 SP - 15 EP - 43 IS - 113-114 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_1984__113-114__15_0/ LA - en ID - AST_1984__113-114__15_0 ER -
Avramov, Luchezar L. Local algebra and rational homotopy, dans Homotopie algébrique et algèbre locale, Astérisque, no. 113-114 (1984), pp. 15-43. https://www.numdam.org/item/AST_1984__113-114__15_0/
[1] , Hopf algebras with divided powers, J. Algebra 18 (1971), 19-50. | MR | Zbl | DOI
[2] , Homologie des Algèbres Commutatives, Springer-Verlag, Berlin, 1979. | Zbl | MR
[3] , Algèbre homologique des anneaux locaux à corps résiduel de caractéristique deux, Lecture Notes in Mathematics 740, 237-242. | MR | Zbl
[4] , Produits de Massey et -ièmes déviations, Lecture Notes in Mathematics 795, 341-359, Springer-Verlag, Berlin, 1980. | MR | Zbl
[5] , Le caractère additif des déviations des anneaux locaux, Comment. Math. Helv. (to appear). | MR | Zbl | EuDML
[6] and , Sullivan's minimal models and higher order Whitehead products, Canad. J. Math. 30 (1978), 961-982. | MR | Zbl | DOI
[7] , Constructions d'espaces de lacets et d'anneaux locaux à séries de Poincaré-Betti non-rationelles, C. R. Acad. Sci. Paris 290(1980), A. 729-733. | Zbl | MR
[8] , A counterexample to a conjecture of Serre, Annals Math, 115, (1982), 1-33. | MR | Zbl
[9] , Jr., On the homology of local rings, Illinois J. Math. 3(1959), 187-199. | MR | Zbl
[10] and , Codimension and multiplicity, Annals Math. 68 (1958), 625-657. | MR | Zbl | DOI
[11] , On the Hopf algebra of a local ring, Isv. Akad. Nauk. SSSR, Ser. mat., 38 (1974), 253-277 | MR | Zbl
, On the Hopf algebra of a local ring English translation : Math. USSR, Izv. 8(1974). | Zbl | MR | DOI
[12] , Homology of local flat extensions and complete intersection defects, Math. Ann. 228(1977), 27-37. | MR | Zbl | EuDML | DOI
[13] , Small homomorphisms of local rings, J. Algebra 50 (1978), 400-453. | MR | Zbl | DOI
[14] , Sur la croissance des nombres de Betti d'un anneau local, C. R. Acad. Sci. Paris 289 (1979), A. 369-372. | MR | Zbl
[15] , Free Lie subalgebras of the cohomology of local rings, Trans. Amer. Math. Soc. 270(1982), 589-608. | MR | Zbl | DOI
[16] , Differential graded models for local rings, RIMS Symposium on Commutative Algebra and Algebraic Geometry (Sept. 10-12, 1981, org. Tadao Oda), | Zbl
, Differential graded models for local rings, RIMS Symposium on Commutative Algebra and Algebraic Geometry RIMS Kokyuroku 446, 80-88, Kyoto University, 1981. | Zbl
[17] , The homology of a tensor product diagram, Reports, Dept. of Maths. Univ. of Stockholm, N° 2, 1982.
[18] , Descente des déviations par homomorphismes locaux et generation des idéaux de dimension projective finie, CR. Acad. Sci. Paris 295 (1982), I. 665-668. | MR | Zbl
[19] , Homotopy Lie algebras for commutative rings and algebras, to appear.
[20] , On real homotopy properties of complete intersections, Izv. Akad. Nauk SSSR, Ser. mat. 43 (1979), 1004-1024; | Zbl | MR
, On real homotopy properties of complete intersections English translation : Math. USSR, Izv. 13(1979). | MR | Zbl
[21] , Algèbre Commutative, Chapitre 3, Hermann, Paris, 1961.
[22] and , On the PL De Rham Theory and rational homotopy type, Memoirs Amer. Math. Soc. 179(1976). | Zbl | MR
[23] , « Jede » endliche freie Auflösung ist freie Auflösung eines von drei Elementen erzeugten Ideals, J. Algebra 39(1976), 429-439. | MR | Zbl | DOI
[24] , Algèbres d'Eilenberg-MacLane, Séminaire H. Cartan, Ecole Normale Supérieure, 1954-1955, Exposés 2 à 11
, Algèbres d'Eilenberg-MacLane, reprinted in Oeuvres, v. III, 1309-1394, Springer-Verlag, Berlin, 1979. | MR
[25] and , The rational homotopy of a wedge, Pacific J. Math. 24 (1968), 241-246. | MR | Zbl | DOI
[26] , , , and , Real homotopy theory of Kähler manifolds, Invent. Math. 29(1975), 245-274. | MR | Zbl | EuDML | DOI
[27] , Homological algebra on a complete intersection with an application to group representations, Trans. Amer. Math. Soc. 260(1980), 35-64. | MR | Zbl | DOI
[28] and , The syzygy problem, Annals Math. 114(1981), 323-333. | MR | Zbl | DOI
[29] and , Category and its applications, Trans. Amer. Math. Soc. 273(1982), 1-37. | Zbl | MR | DOI
[30] , and , The homotopy Lie algebra for finite complexes, Publ. Math. IHES 56 (1982), 179-202. | DOI | MR | Zbl | EuDML | Numdam
[31] and , The radius of convergence of Poincaré series of loop spaces, Invent. Math. 68(1982), 257-274. | MR | Zbl | EuDML | DOI
[32] and , Some reduction formulas for the Poincaré series of modules, Atti. Accad. naz. Lincei. VIII Ser., Rend. Cl. Sci. Fis.mat.natur. 58(1975), 82-91. | MR | Zbl
[33] and , Increasing sequences of Betti numbers, Pacific J. Math. 87(1980), 65-68. | Zbl | MR | DOI
[34] , A homological characterization of local complete intersections, Compositio Math. 23 (1971), 251-255. | MR | Zbl | EuDML | Numdam
[35] , A change of rings theorem with applications to Poincaré series and intersection multiplicity, Math. Scand. 34(1974), 167-183. | MR | Zbl | EuDML | DOI
[36] , On the deviations of a local ring, Math. Scand. 47(1980), 5-20. | MR | Zbl | EuDML | DOI
[37] and , Homology of Local Rings, Queen's papers in Pure and Applied Mathematics - No. 20, Queen's University, Kingston, Ontario, 1969. | MR | Zbl
[38] , Rational fibrations, minimal models, and fibrings of homogeneous spaces, Trans. Amer. Math. Soc. 244(1978), 199-224. | MR | Zbl | DOI
[39] , Lectures on Minimal Models, Pub. IRMA-Lille, V. 3, Fasc. 4 (1981), (3rd Edition). | MR | Zbl
[40] , On flat homomorphisms and the Yoneda Ext-algebra of the fibre, these Proceedings.
[41] , Théorie homotopique des formes différentielles, Astérisque 45(1977). | MR | Zbl
[42] , Anneaux locaux et espaces de lacets à séries de Poincaré non-rationnelles, Séminaire Bourbaki, 1980-81, No. 570, Lecture Notes in Mathematics 901, Springer-Verlag, Berlin, 1981. | MR | Zbl | EuDML | Numdam
[43] , Homology of local rings, Ph.D. Thesis, Univ. of Chicago, 1965. | MR
[44] , Local rings and Golod homomorphisms, J. Algebra 37(1975), 266-289. | MR | Zbl | DOI
[45] , Finitely-generated Ext-algebras, Math. Scand. 49 (1981), 161-180. | MR | Zbl | EuDML | DOI
[46] and , Factoring out the socle of a local Gorenstein ring, J. Algebra 55(1978), 74-83. | MR | Zbl | DOI
[47] , On the subalgebra generated by the one-dimensional elements of the Yoneda Ext-algebra, Reports, Dept. of Maths., Univ. of Stockholm, No. 5, 1976. | Zbl
[48] et , Cohomologie des algèbres de Lie graduées et séries de Poincaré-Betti non rationelles, C. R. Acad. Sci. Paris 290(1980), A. 733-736. | MR | Zbl
[49] , Commutative Algebra (2nd edition), Benjamin/Cummings, Reading, Mass, 1980. | MR
[50] , On the formality of -connected compact manifolds of dimension less than or equal to 4k - 2, Illinois J. Math. 23 (1979), 253-258. | MR | Zbl
[51] and , On the structure of Hopf algebras, Annals Math. 81(1965), 211-264. | MR | Zbl | DOI
[52] , Algèbre homologique et homologie des espaces classifiants, Séminaire H. Cartan, Ecole Normale Supérieure, 1959-1960, Exposé 7, | Zbl | EuDML | Numdam
, Algèbre homologique et homologie des espaces classifiants, Secrétariat Math., Paris, 1961. | Zbl | Numdam
[53] , The rational homotopy groups of complete intersections, Illinois J. Math. 23 (1979), 175-182. | MR | Zbl
[54] , Deformations of Complex spaces, Uspehi Mat. Nauk 31, No. 3 (1976), 129-194, (in Russian) | MR | Zbl
, Deformations of Complex spaces English translation: Rusian Math. Surveys 31(1976). | Zbl | MR
[55] , On the (co-)homology of commutative rings, Proc. Symp. Pure Math. 17, 65-87, | MR | Zbl | DOI
, On the (co-)homology of commutative rings, Amer. Math. Soc., Providence, 1970. | MR | Zbl
[56] , Betti numbers and reflexive modules, in Ring Theory (R. Gordon, Ed.), 297-308, Academic Press, NY, 1972. | MR | Zbl | DOI
[57] , Sequences of Betti numbers, J. Algebra 66(1980), 193-204. | MR | Zbl | DOI
[58] , Relations between the Poincaré-Betti series of loop spaces and of local rings, Lecture Notes in Mathematics 740, 285-322, Springer-Verlag, Berlin, 1979. | Zbl | MR
[59] , Homology of loop spaces and of local rings, in Proceedings 18th Scandinavian Congress of Mathematics, 1980 | Zbl
, Homology of loop spaces and of local rings, Progress in Mathematics 11, 441-468, Birkhäuser, Basel, 1981. | MR | Zbl
[60] , The use of graded Lie algebras in the theory of local rings, Proc. Durham Conf. in Commutative Algebra, 1981, | Zbl
, The use of graded Lie algebras in the theory of local rings London Math. Soc. Lecture Notes, 72,204-230, Cambridge University Press, 1982. | Zbl | MR
[61] , Homologie des anneaux locaux noethériens, C. R. Acad. Sci. Paris 265(1967), A. 768-771. | MR | Zbl
[62] , Algèbre locale.Multiplicités, Lecture Notes in Mathematics 11 (3e edition), Springer-Verlag, Berlin, 1975. | Zbl
[63] , A set of generators for Ext, Math. Scand. 38(1967), 1-12. | MR | Zbl | EuDML
[64] , Hopf algebras and derivations, J. Algebra 64(1980), 218-229. | MR | Zbl | DOI
[65] , Rational Poincaré duality spaces, Preprint, 1981. | MR | Zbl
[66] , Infinitesimal computations in topology, Publ. Math. IHES 47 (1978), 269-331. | DOI | MR | Zbl | EuDML | Numdam







