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Stiefel-Whitney Classes of a Symmetric Bilinear Form — A Formula of Serre

Published online by Cambridge University Press:  20 November 2018

Victor Snaith
Victor Snaith*
Affiliation:
Department of Mathematics, The University of Western OntarioLondon, Ontario, Canada N6A 5B7
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Abstract

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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.

Keywords

10C0512G0555R40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 2 , 01 June 1985 , pp. 218 - 222
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Atiyah, M.F., Bott, R. and Shapiro, A., Clifford modules, Topology, 3 (1964), pp. 3–38.Google Scholar
2. Conner, P. and Pedis, R., The Witt class of a trace form, L.S.U. preprints (1983).Google Scholar
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. 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. Husemoller, D., Fibre Bundles, Mc-Graw Hill (1968).Google Scholar
6. Milnor, J.W., Algebraic K-theory and quadratic forms, Inventiones Math., 9 (1970), pp. 318–344.Google Scholar
7. Milnor, J.W. and Husemoller, D., Symmetric bilinear forms, Ergeb. Math., No. 73 (1973), Springer-Verlag.Google Scholar
8. Milnor, J.W. and Stasheff, J.D., Characteristic classes, Annals of Math. Studies, No. 76.Google Scholar
9. O'Meara, O. T., Introduction to quadratic forms, Grund Math. Wiss., No. 117 (1973), Springer-Verlag.Google Scholar
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. Serre, J-P., Cohomologie Galoisienne, Lecture Notes in Mathematics, No. 5 (1973), Springer-Verlag.Google Scholar
12. Serre, J-P., Local fields, Grad. Texts in Math., No. 67, Springer-Verlag.Google Scholar
13. Serre, J-P., L'invariant de Witt de la forme Tr(x)2, to appear in Comm. Math. Helveticii.Google Scholar