Modules quadratiques
Mémoires de la Société Mathématique de France (1979)
- Volume: 63, page 5-144
- ISSN: 0249-633X
Access Full Article
topHow to cite
topMicali, A., and Revoy, Ph.. "Modules quadratiques." Mémoires de la Société Mathématique de France 63 (1979): 5-144. <http://eudml.org/doc/94810>.
@article{Micali1979,
author = {Micali, A., Revoy, Ph.},
journal = {Mémoires de la Société Mathématique de France},
keywords = {review article; generalisation to commutative rings; Witt group; Clifford algebra; graded Brauer group; survey; vector products; Cayley algebras; algebraic Stiefel varieties; unique factorization; Stiefel Whitney classes; semilocal rings; quadratic forms over fields},
language = {fre},
pages = {5-144},
publisher = {Société mathématique de France},
title = {Modules quadratiques},
url = {http://eudml.org/doc/94810},
volume = {63},
year = {1979},
}
TY - JOUR
AU - Micali, A.
AU - Revoy, Ph.
TI - Modules quadratiques
JO - Mémoires de la Société Mathématique de France
PY - 1979
PB - Société mathématique de France
VL - 63
SP - 5
EP - 144
LA - fre
KW - review article; generalisation to commutative rings; Witt group; Clifford algebra; graded Brauer group; survey; vector products; Cayley algebras; algebraic Stiefel varieties; unique factorization; Stiefel Whitney classes; semilocal rings; quadratic forms over fields
UR - http://eudml.org/doc/94810
ER -
References
top- [1] J.F. Adams, Vector fields on spheres, Ann. of Math. 75 (1962), 603-632. Zbl0112.38102MR25 #2614
- [2] C. Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2, Journal für R. und A. Math. 183 (1941), 148-167. Zbl0025.01403MR4,237fJFM67.0055.02
- [3] M. Auslander and O. Goldman, The Brauer group of a commutative ring, Transactions of the A.M.S. 97 (1960), 367-409. Zbl0100.26304MR22 #12130
- [4] A. Bak, K-theory of forms, Annals of Math. Studies, Princeton. Zbl0465.10013
- [5] H. Bass, Lectures on Topics in Algebraic K-theory, Tata Institute of Fundamental Research, Bombay 1967. Zbl0226.13006MR43 #4885
- [6] H. Bass, K-theorie and stable algebra, Publications Mathématiques I.H.E.S. n° 22, pages 1-60. Zbl0248.18025
- [7] H. Bass, Unitary algebraic K-theory, Lecture Notes in Math. 343 (1973), 57-265, Springer-Verlag. Zbl0299.18005MR51 #8211
- [8] H. Bass, Clifford algebras and spinor norms over a commutative ring, Amer. J. Math. 46 (1974), 156-206. Zbl0344.15017MR50 #13092
- [9] Z.I. Borevitch et I.R. Chafarevitch, Théorie des Nombres, Gauthier-Villars, Paris, 1967. Zbl0145.04901MR34 #5734
- [10] N. Bourbaki, Algèbre, Chap. 9. Hermann, Paris 1973.
- [11] N. Bourbaki, Algèbre Commutative, Chap. 1 et 2, Hermann, Paris 1961. Zbl0108.04002
- [12] N. Bourbaki, Algèbre, Chap. 1 à 3, Hermann, Paris 1970. Zbl0211.02401
- [13] N. Bourbaki, Algèbre Commutative, Chap. 7, Hermann, Paris 1965. Zbl0141.03501
- [14] R.R. Brown and A. Gray, Vector cross products, Comm. Math. Helv. 41 (1967), 222-236. Zbl0155.35702MR36 #5157
- [15] T.C. Craven, A. Rosenberg and R. Ware, The map of the Witt ring of a domain into the Witt ring of its field of fractions, Proc. Amer. Math. Soc. 51 (1975), 25-30. Zbl0313.13025MR52 #5662
- [16] A. Delzant, Définition des classes de Stiefel-Whitney d'un module quadratique sur un corps de caractéristique différente de 2, C.R. Acad. Sci. Paris 255 (1962), 1366-1368. Zbl0108.04303MR26 #175
- [17] J. Dieudonné, Sur les groupes classiques, Hermann, Paris, 1958.
- [18] B. Eckmann, Stetige Lösungen linearer Gleichungsysteme, Comm. Math. Helv. 15 (1942-1943), 318-339. Zbl0028.32001MR5,104h
- [19] M. Eichler, Quadratische Formen und orthogonale Gruppen, Springer-Verlag, 1952. Zbl0049.31106MR14,540a
- [20] R. Fossum, The divisor class group of a Krull domain, Ergebnisse der Mathematik, Band 74, Springer-Verlag 1973. Zbl0256.13001MR52 #3139
- [21] A. Grothendieck, Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968.
- [22] C. Hostmaelingen, Sur l'anneau de Witt d'un anneau de Prüfer, C.R. Acad. Sci. Paris 280 (1975), 69-71. Zbl0301.13015MR53 #412
- [23] C. Hostmaelingen, Sur l'anneau de Witt d'un anneau semi-héréditaire, Anais da Academia Brasileira de Ciências, à paraître.
- [24] E. Hornix, Stiefel-Whitney invariants of quadratic forms over local rings, J. of Algebra 26 (1973), 258-279. Zbl0263.18014MR49 #219
- [25] I. Kaplansky and R. Shaker, Abstract quadratic forms, Canadian Journal of Math. 21 (1969), 1218-1233. Zbl0238.15010MR40 #2701
- [26] O. Laborde, Formes quadratiques, algèbres de Clifford et signatures, C.R. Acad. Sci. Paris 278 (1974), 1599-1602. Zbl0301.13016MR50 #13004
- [27] T.Y. Lam, The algebraic theory of quadratic forms, W.R. Benjamin, Inc., Reading 1973. Zbl0259.10019MR53 #277
- [28] A. Larotonda, A. Micali et O.E. Villamayor, Sur le groupe de Witt, Symposia Mathematica 11 (1973), 211-219. Zbl0298.13017MR50 #7128
- [29] D. Legrand, Formes quadratiques et algèbres quadratiques, Thèse de doctorat, n° d'ordre C.N.R.S. 803, 1971.
- [30] F. Lorenz, Quadratische Formen über Körpern, Lecture Notes in Math. 130, Springer-Verlag 1970. Zbl0211.35303MR44 #189
- [31] A. Micali et O.E. Villamayor, Sur les algèbres de Clifford, Ann. Sc. Ec. Normale Sup. 1 (1968), 271-304. Zbl0182.05304MR41 #244
- [32] A. Micali et O.E. Villamayor, Sur les algèbres de Clifford II, Journal für R. und A. Math., 242 (1970), 61-90. Zbl0252.15015MR41 #6902
- [33] A. Micali et O.E. Villamayor, Algèbres de Clifford et groupe de Brauer, Ann. Sc. Ec. Normale Sup. 4 (1971), 285-310. Zbl0252.15016MR45 #1956
- [34] J. Milnor, On simply connected manifolds, Symp. Mexico (1958), 122-128. Zbl0105.17204MR21 #2240
- [35] J. Milnor, Algebraic K-theory and quadratic forms, Inventiones Math. 9 (1970), 318-344. Zbl0199.55501MR41 #5465
- [36] J. Milnor and D. Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik, Band 73, Springer-Verlag 1973. Zbl0292.10016MR58 #22129
- [37] A. Morris, On a generalized Clifford algebra (II), Quart. Journal of Math. 19 (1968), 289-299. Zbl0169.35903MR38 #173
- [38] Y. Nouazé et Ph. Revoy, Algèbres de Weyl généralisées, Bull. Sc. Math. 96 (1972), 27-47. Zbl0261.16011MR46 #9110
- [39] T. Ogama, On a problem of Fossum, Proc. Japan Academy 50 (1974), 266-267. Zbl0305.13013MR50 #13011
- [40] O.T. O'Meara, Introduction to quadratic forms, Springer-Verlag, 1963. Zbl0107.03301MR27 #2485
- [41] A. Pfister, Quadratische Formen in beliebigen Körpern, Inventiones Math. 1 (1966), 116-132. Zbl0142.27203MR34 #169
- [42] Ph. Revoy, Sur les deux premiers invariants d'une forme quadratique, Ann. Sc. Ec. Normale Sup. 4 (1971), 311-319. Zbl0231.15020MR44 #6735
- [43] Ph. Revoy, Groupes de Witt d'un corps de caractéristique 2, Journal für R. und A. Math. 296 (1977), 33-36. Zbl0356.12023MR56 #15681
- [44] Ph. Revoy, Autour des formes quadratiques, thèse de doctorat, N° d'enregistrement au C.N.R.S. A.O. 8580, Université de Montpellier II, 1975.
- [45] A. Roy, Cancellation of quadratic forms over commutative rings, J. of Algebra 10 (1968), 286-298. Zbl0181.04302MR38 #172
- [46] P. Samuel, Lectures on unique factorization domains, Tata Institut of Fundamental Research, Bombay, 1964. Zbl0184.06601MR35 #5428
- [47] W. Scharlau, Quadratische Formen und Galois Cohomologie, Inventiones Math. 4 (1967), 238-264. Zbl0165.35802MR37 #1442
- [48] W. Scharlau, Quadratic reciprocity laws, Journal of Number Theory 4 (1972), 78-97. Zbl0241.12005MR45 #1835
- [49] J.P. Serre, Modules projectifs et espaces fibrés à fibre vectorielle, Séminaire P. Dubreil 1957/1958, Exposé 23 du 5 mai 1958. Zbl0132.41202
- [50] J.P. Serre, Corps locaux, Hermann, Paris 1968. Zbl0137.02601MR50 #7096
- [51] J.P. Serre, Cours d'Arithmétique, PUF, Paris 1970. Zbl0225.12002MR41 #138
- [52] C. Small, The Brauer group of a commutative ring, Transactions of the A.M.S. 156 (1971), 455-491. Zbl0216.32501MR43 #1966
- [53] U. Tietze, Zur theorie quadratischer Formen über Körpern der Charakteristik 2, Journal für R. und A. Math., 268-269 (1974), 388-390. Zbl0293.15025MR50 #7029
- [54] O.E. Villamayor, Separable algebras and Galois extensions, Osaka J. Math. 4 (1967), 161-171. Zbl0168.28802MR37 #4064
- [55] G. Vranceanu, Sur les vecteurs tangents aux sphères, Revue Roumaine de Math. Pures et Appliquées 10 (1965), 895-914. Zbl0145.20204MR34 #5103
- [56] C.T.C. Wall, Graded Brauer groups, Journal dür R. und A. Math., 213 (1964), 187-199. Zbl0125.01904MR29 #4771
- [57] G.W. Whitehead, Note on cross sections in Stiefel manifolds, Comm. Math. Helv. 37 (1963), 239-240. Zbl0118.18702MR26 #5583
- [58] E. Witt, Theorie der quadratischen. Formen in beliebigen Körpern, Journal für R. und A. Math. 176 (1937), 31-44. Zbl0015.05701JFM62.0106.02
- [59] P. Zvengrovoski, A 3-fold vector product in R8, Comm. Math. Helv. 40 (1966), 148-152. Zbl0134.38401
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.