Stiefel-Whitney Classes of a Symmetric Bilinear Form — A Formula of Serre
Canadian mathematical bulletin, Tome 28 (1985) no. 2, pp. 218-222

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a field of characteristic different from two. Let L be a finite separable extension of K. If is the separable closure of K, we have a continuous homomorphism π : Ga(/K) → ∑n(n - [L : K]). We give a very short proof of Serre's formula which evaluates the Hasse-Witt invariant of a symmetric bilinear form, transferred from L, in terms of the topological Stiefel-Whitney classes of IT.
DOI : 10.4153/CMB-1985-025-2
Mots-clés : 10C05, 12G05, 55R40
Snaith, Victor. Stiefel-Whitney Classes of a Symmetric Bilinear Form — A Formula of Serre. Canadian mathematical bulletin, Tome 28 (1985) no. 2, pp. 218-222. doi: 10.4153/CMB-1985-025-2
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[1] 1. Atiyah, M.F., Bott, R. and Shapiro, A., Clifford modules, Topology, 3 (1964), pp. 3–38. Google Scholar

[2] 2. Conner, P. and Pedis, R., The Witt class of a trace form, L.S.U. preprints (1983). Google Scholar

[3] 3. Delzant, M.A., Définition des classes de Stief el-Whitney d'un module quadratique sur un corps de charactéristique differente de 2, C. R. Acad. Sri., Paris, 255 (1962), pp. 1366–1368. Google Scholar

[4] 4. Fiedorowicz, Z. and S. B. Priddy. Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Mathematics, No. 674 (1978), Springer-Verlag. Google Scholar

[5] 5. Husemoller, D., Fibre Bundles, Mc-Graw Hill (1968). Google Scholar

[6] 6. Milnor, J.W., Algebraic K-theory and quadratic forms, Inventiones Math., 9 (1970), pp. 318–344. Google Scholar

[7] 7. Milnor, J.W. and Husemoller, D., Symmetric bilinear forms, Ergeb. Math., No. 73 (1973), Springer-Verlag. Google Scholar

[8] 8. Milnor, J.W. and Stasheff, J.D., Characteristic classes, Annals of Math. Studies, No. 76. Google Scholar

[9] 9. O'Meara, O. T., Introduction to quadratic forms, Grund Math. Wiss., No. 117 (1973), Springer-Verlag. Google Scholar

[10] 10. Quillen, D.G., The mod 2 cohomology ring of extra-special 2-groups, the Spinor groups, Math. Ann., 94 (1971), pp. 197–212. Google Scholar

[11] 11. Serre, J-P., Cohomologie Galoisienne, Lecture Notes in Mathematics, No. 5 (1973), Springer-Verlag. Google Scholar

[12] 12. Serre, J-P., Local fields, Grad. Texts in Math., No. 67, Springer-Verlag. Google Scholar

[13] 13. Serre, J-P., L'invariant de Witt de la forme Tr(x)2, to appear in Comm. Math. Helveticii. Google Scholar

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