Extensions du groupe additif

Breen, Lawrence

Breen, Lawrence

Publications Mathématiques de l'IHÉS, Tome 48 (1978), pp. 39-125.

MR Zbl | 3 citations dans Numdam

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     author = {Breen, Lawrence},
     title = {Extensions du groupe additif},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {39--125},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {48},
     year = {1978},
     mrnumber = {516914},
     zbl = {0404.14018},
     language = {fr},
     url = {http://www.numdam.org/item/PMIHES_1978__48__39_0/}
}

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%J Publications Mathématiques de l'IHÉS
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Breen, Lawrence. Extensions du groupe additif. Publications Mathématiques de l'IHÉS, Tome 48 (1978), pp. 39-125. http://www.numdam.org/item/PMIHES_1978__48__39_0/

Bibliographie
Cité par

[1] J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, Chicago-London, The University of Chicago Press (1974). | MR | Zbl

[2] D. W. Anderson, Simplicial K-theory and generalised homology theories I, II, à paraître.

[3] M. Artin, A. Grothendieck et J.-L. Verdier, Théorie des topos et cohomologie étale des schémas (SGA 4), Lecture Notes in Mathematics, 269, 270, 305, Berlin-Heidelberg-New York, Springer (1972-1973).

[4] J. Boardman, Stable homotopy theory. Notes multigraphiées de l'Université de Warwick (à partir de 1965).

[5] J. Boardman et R. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, 347, Berlin-Heidelberg-New York, Springer (1973). | MR | Zbl

[6] A. K. Bousfield, Homogeneous functors and their derived functors, notes multigraphiées, M.I.T.

[7] A. K. Bousfield, Operations on derived functors of non-additive functors, notes multigraphiées, M.I.T.

[8] G. Bredon, Sheaf theory, New York, McGraw-Hill (1967). | MR | Zbl

[9] L. Breen, Extensions of abelian sheaves and Eilenberg-Mac Lane algebras, Invent. Math., 9 (1969), 15-44. | MR | Zbl

[10] L. Breen, On a non trivial higher extension of representable abelian sheaves, Bull. Amer. Math. Soc., 75 (1969), 1249-1253. | MR | Zbl

[11] L. Breen, Un théorème d'annulation pour certains des Exti de faisceaux abéliens, Ann. Scient. Ec. Norm. Sup., 8 (1975), 339-352. | Numdam | MR | Zbl

[12] K. S. Brown, Abstract homotopy theory and generalised sheaf cohomology, Trans. Amer. Math. Soc., 186 (1974), 419-458. | MR | Zbl

[13] H. Cartan, Algèbres d'Eilenberg-Mac Lane et homotopie (Séminaire Cartan 1954-1955), New York-Amsterdam, W. A. Benjamin (1967). | Zbl

[14] A. Clark, Homotopy commutativity and the Moore spectral sequence, Pacific J. Math., 15 (1965), 65-74. | MR | Zbl

[15] J. M. Cohen, Stable homotopy, Lecture Notes in Mathematics, 165, Berlin-Heidelberg-New York, Springer (1970). | MR | Zbl

[16] J. M. Cohen, The Hurewicz homomorphism on MU, Invent. Math., 10 (1970), 177-186. | MR | Zbl

[17] P. Deligne, Théorie de Hodge III, Publ. Math. I.H.E.S., 44 (1974), 5-77. | Numdam | MR | Zbl

[18] M. Demazure et P. Gabriel, Groupes algébriques (t. I), Amsterdam, North-Holland Publishing Co. (1970). | Zbl

[19] M. Demazure et A. Grothendieck, Schémas en groupes (SGA 3) I, Lecture Notes in Mathematics, 151, Berlin-Heidelberg-New York, Springer (1970). | MR | Zbl

[20] A. Dold, Über die Steenrodschen Kohomologieoperationen, Ann. of Math., 73 (1961), 258-294. | MR | Zbl

[21] A. Dold et D. Puppe, Homologie nicht-additiver Functoren, Anwendungen, Ann. Inst. Fourier, 11 (1961), 201-312. | Numdam | MR | Zbl

[22] E. Dyer et R. Lashof, Homology of iterated loop spaces, Am. J. Math., 84 (1962), 35-88. | MR | Zbl

[23] G. Efroymson, A study of H3sym(A, M), J. of Algebra, 14 (1970), 24-34. | MR | Zbl

[24] S. Eilenberg et S. Mac Lane, Homology theory for multiplicative systems, Trans. Amer. Math. Soc., 71 (1951), 294-330. | MR | Zbl

[25] S. Eilenberg et S. Mac Lane, On the groups H(II, n) I, II, Ann. of Math., 58, 55-106 et 60 (1954), 49-139. | MR | Zbl

[26] S. Eilenberg et S. Mac Lane, On the homology theory of abelian groups, Canadian J. Math., 7 (1955), 43-53. | MR | Zbl

[27] D. B. A. Epstein, Steenrod operations in homological algebra, Invent. Math., 1 (1966), 152-208. | MR | Zbl

[28] P. Gabriel et M. Zisman, Calculus of fractions and homotopy theory. Ergebnisse der Mathematik und ihre Grenzgebiete, New Series, Vol. 35, Berlin-Heidelberg-New York, Springer (1967). | MR | Zbl

[29] R. Godement, Théorie des faisceaux. Actualités scientifiques et industrielles, 1252, Paris, Hermann (1964).

[30] A. Grothendieck et J. Dieudonné, Éléments de géométrie algébrique (EGA III), Étude cohomologique des faisceaux cohérents (première partie), Publ. Math. I.H.E.S., 11 (1961). | Numdam | Zbl

[31] A. Grothendieck, Groupes de monodromie en géométrie algébrique (SGA 7) I, Lecture Notes in Mathematics, 288, Berlin-Heidelberg-New York, Springer (1972). | MR | Zbl

[32] H. Hastings, A smash product for spectra, Bull. Amer. Math. Soc., 79 (1973), 946-951. | MR | Zbl

[33] R. Heaton, Polynomial 3-cocycles over fields of characteristic p, Duke Math. J., 26 (1959), 269-275. | MR | Zbl

[34] L. Illusie, Complexe cotangent et déformations I, II, Lecture Notes in Mathematics, 239, 283, Berlin-Heidelberg-New York, Springer (1972). | Zbl

[35] D. Kan, Semisimplicial spectra, Illinois J. Math., 7 (1963), 463-478. | MR | Zbl

[36] D. Kan et G. W. Whitehead, The reduced join of two spectra, Topology, 3, supplement 2 (1965), 239-261. | MR | Zbl

[37] S. Kochman, Symmetric Massey products and a Hirsch formula in homology, Trans. Amer. Math. Soc., 163 (1972), 245-260. | MR | Zbl

[38] D. Kraines, The A(p) cohomology of some k-stage Postnikov systems, Comment. Math. Helv., 48 (1973), 56-71. | MR | Zbl

[39] K. Lamotke, Semisimpliziale algebraische Topologie. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 147, Berlin-Heidelberg-New York, Springer (1968). | MR | Zbl

[40] M. Lazard, Lois de groupe et analyseurs, Ann. Scient. Éc. Norm. Sup., 72 (1955), 299-400. | Numdam | MR | Zbl

[41] J. Lubin et J. Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France, 94 (1966), 49-59. | Numdam | MR | Zbl

[42] S. Mac Lane, The homology products in K(II, n), Proc. Amer. Math. Soc., 5 (1954), 642-651. | MR | Zbl

[43] S. Mac Lane, Homologie des anneaux et des modules, C.B.R.M. Louvain (1956), 55-80. | MR | Zbl

[44] S. Mac Lane, Homology. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 114, Berlin-Heidelberg-New York, Springer (1963). | MR | Zbl

[45] J. P. May, The cohomology of augmented algebras and generalised Massey products for DGA algebras, Trans. Amer. Math. Soc., 122 (1966), 334-340. | MR | Zbl

[46] J. P. May, A general algebraic approach to Steenrod operations. Paru dans : The Steenrod Algebra and its applications, Lecture Notes in Mathematics, 168, Berlin-Heidelberg-New York, Springer (1970). | MR | Zbl

[47] R. Milgram, Steenrod squares and higher Massey products, Bol. Soc. Math. Mexicana, 13 (1968), 32-57. | MR | Zbl

[48] J. Milne, Duality in the flat cohomology of a surface, Ann. Scient. Éc. Norm. Sup., 9 (1976), 171-202. | Numdam | MR | Zbl

[49] J. Milnor, The Steenrod algebra and its dual, Ann. of Math., 67 (1958), 150-171. | MR | Zbl

[50] G. Nishida, Cohomology operations in iterated loop spaces, Proc. Japan Acad., 44 (1968), 104-109. | MR | Zbl

[51] F. Oort, Commutative group schemes, Lecture Notes in Mathematics, 15, Berlin-Heidelberg-New York, Springer (1966). | MR | Zbl

[52] S. Priddy, Mod p right derived functor algebras of the symmetric algebra functor, J. Pure and Applied Algebra, 3 (1973), 337-356. | MR | Zbl

[53] D. Quillen, Homotopical algebra, Lecture Notes in Mathematics, 43, Berlin-Heidelberg-New York, Springer (1967). | MR | Zbl

[54] D. Quillen, On the homology theory of commutative rings, notes multigraphiées, M.I.T. | Zbl

[55] D. Quillen, On the (co-)homology of commutative rings. Paru dans : Applications of Categorical algebra (Proc. Symp. Pure Math. XVII), 65-87 ; Providence, Amer. Math. Soc. (1970). | MR | Zbl

[56] M. Raynaud, Modules projectifs universels, Invent. Math., 6 (1968), 1-26. | MR | Zbl

[57] N. Roby, Lois polynômes et lois formelles en théorie des modules, Ann. Scient. Éc. Norm. Sup., 80 (1963), 213-348. | Numdam | MR | Zbl

[58] M. Rothenberg et N. Steenrod, The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc., 71 (1965), 872-875. | MR | Zbl

[59] G. Segal, Classifying spaces and spectral sequences, Publ. Math. I.H.E.S., 34 (1968), 105-112. | Numdam | MR | Zbl

[60] G. Segal, The multiplicative group of classical cohomology, Quarterly J. Math., 26 (1975), 289-293. | MR | Zbl

[61] J.-P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-Mac Lane, Comment. Math. Helv., 27 (1953), 198-232. | MR | Zbl

[62] J.-P. Serre, Groupes algébriques et corps de classes, Actualités scientifiques et industrielles, 1264, Paris, Hermann (1959). | Zbl

[63] Hong Xuan Sinh, Gr-catégories, thèse, Université Paris VII (1975).

[64] J. Stasheff, Homotopy associativity of H-spaces II, Trans. Amer. Math. Soc., 108 (1963), 293-312. | MR | Zbl

[65] N. Steenrod et D. B. A. Epstein, Cohomology operations, Annals of Mathematics Studies, 50, Princeton, Princeton University Press (1962). | MR | Zbl

[66] M. Tierney, Categorical constructions in stable homotopy, Lecture Notes in Mathematics, 87, Berlin-Heidelberg-New York, Springer (1969). | MR | Zbl

[67] R. Vogt, Boardman's stable homotopy category, Aarhus Universitet Lecture Notes, 21, notes multigraphiées (1971). | MR | Zbl

[68] G. W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc., 102 (1962), 227-283. | MR | Zbl