Abstract
LetF be a field of characteristic 2. The aim of this paper is to study the isotropy of someF-quadratic forms of dimension ≤6 over the function field of a projective quadric.
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Références
A. A. Albert,Structure of Algebras, American Mathematical Society Colloquium PublicationXXIV, 1939.
R. Baeza,Ein Teilformensatz für quadratische Formen in Charakteristik 2, Mathematische Zeitschrift135 (1974), 175–184.
R. Baeza,Quadratic forms over semilocal rings, Lecture Notes in Mathematics655, Springer, Berlin, Heidelberg, New York, 1978.
R. Baeza,Common splitting rings of quaternion algebras over semi-local rings, inProceedings of the 1976 Conference on Quadratic Forms (G. Orzech, ed.), Queen’s Papers in Pure and Applied Mathematics46, Queens University, Kingston, Ontario, 1977, pp. 373–376.
R. Baeza,The norm theorem for quadratic forms over a field of characteristic 2, Communications in Algebra18 (1990), 1337–1348.
R. W. Fitzgerald,Witt kernels of functions fields extensions, Pacific Journal of Mathematics109 (1983), 89–106.
D. W. Hoffmann,Isotropy of 5-dimensional quadratic forms over the function field of a quadric, Proceedings of Symposia in Pure Mathematics, Vol. 58, AMS Summer Research Institute, Santa Barbara, 1992, pp. 217–225.
D. W. Hoffmann,On 6-dimensional quadratic forms isotropic over the function fields of a quadric, Communications in Algebra22 (1994), 1999–2014.
D. W. Hoffmann,Isotropy of quadratic forms over the function field of a quadric, Mathematische Zeitschrift220 (1995), 461–476.
D. W. Hoffmann,On quadratic forms of height two and a theorem of Wadsworth, Transactions of the American Mathematical Society348 (1996), 3267–3281.
O. T. Izhboldin and N. A. Karpenko,Isotropy of 6-dimensional quadratic forms over function fields of quadrics, Journal of Algebra209 (1998), 65–93.
O. T. Izhboldin and N. A. Karpenko,Isotropy of virtual Albert forms over function fields of quadrics, Mathematische Nachrichten206 (1999), 111–122.
N. Jacobson,Some applications of Jordan norms to involutorial simple associative algebras, Advances in Mathematics48 (1983), 149–165.
M. Knebusch,Specialization of quadratic and symmetric bilinear forms, and a norm theorem, Acta Arithmetica24 (1973), 279–299.
M.-A. Knus,Sur la forme d’Albert et le produit tensoriel de deux algèbres de quaternions, Bulletin de la Société Mathématique de Belgique-Tijdsch. Belg. Wisk. Gen. 453, Ser. B (1993), 333–337.
A. Laghribi,Isotropie de certaines formes quadratiques de dimensions 7 et 8 sur le corps des fonctions d’une quadrique, Duke Mathematical Journal85 (1996), 397–410.
A. Laghribi,Formes quadratiques en 8 variables dont l’algèbre de Clifford est d’indice 8, K-Theory12 (1997), 371–383.
A. Laghribi,Formes quadratiques de dimension 6, Mathematische Nachrichten204 (1999), 125–135.
A. Laghribi et P. Mammone,Isotropie d’une forme quadratique sur le corps des fonctions d’une quadrique en caractéristique 2, à paraître dans Bulletin de la Société Mathématique de Belgique.
D. Leep,Function fields results, notes manuscrites prises par T. Y. Lam, 1989.
P. Mammone,Similitude de formes quadratiques et corps de fonctions en caractéristique 2, Bulletin de la Société Mathématique de Belgique39 (1987), 373–377.
P. Mammone, R. Moresi and A. Wadsworth,u-Invariant of fields of characteristics 2, Mathematische Zeitschrift208 (1991), 335–347.
P. Mammone and D. Shapiro,The Albert quadratic form for an algebra of degree four, Proceedings of the American Mathematical Society105 (1989), 525–530.
P. Mammone, J.-P. Tignol and A. Wadsworth,Fields of characteristic 2with prescribed u-invariant, Mathematische Annalen290 (1991), 109–128.
A. S. Merkur’ev,Simple algebras and quadratic forms (en Russe), Izvestiya Akademii Nauk SSSR55 (1991), 218–224. Traduction anglaise: Mathematics of the USSR-Izvestiya38 (1992), 215–221.
W. Scharlau,Quadratic and Hermitian Forms, Grundlehren der Mathematischen Wissenschaften, Bd. 270, Springer, Berlin, Heidelberg, New York, Tokyo, 1985.
D. Shapiro,Similarities, quadratic forms, and Clifford algebras, Thesis, University of California, Berkeley, 1974.
T. A. Springer,Quadratic forms over fields with a discrete valuation I, Indagationes Mathematicae17 (1955), 352–362.
J. Tits,Sur les produits tensoriels de deux algèbres de quaternions, Bulletin de la Société Mathématique de Belgique-Tijdsch. Belg. Wisk. Gen. 453, Ser. B (1993), 329–331.
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Laghribi, A. Certaines formes quadratiques de dimensin au plus 6 et corps des fonctions en caractéristique 2. Isr. J. Math. 129, 317–361 (2002). https://doi.org/10.1007/BF02773169
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DOI: https://doi.org/10.1007/BF02773169