Geodesic
Isotropy of quadratic spaces in finite and infinite dimension
Documenta mathematica, Tome 12 (2007), pp. 473-504.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In the late 1970s, Herbert Gross asked whether there exist fields admitting anisotropic quadratic spaces of arbitrarily large finite dimensions but none of infinite dimension. We construct examples of such fields and also discuss related problems in the theory of central simple algebras and in Milnor $K$-theory.
Classification : 11E04, 11E81, 12D15, 12E15, 12F20, 12G05, 12G10, 16K20, 19D45
Keywords: quadratic form, isotropy, infinite-dimensional quadratic space, $u$-invariant, function field of a quadric, totally indefinite form, real field, division algebra, quaternion algebra, symbol algebra, Galois cohomology, cohomological dimension, Milnor $K$-theory 
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     title = {Isotropy of quadratic spaces in finite and infinite dimension},
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Becher, Karim Johannes; Hoffmann, Detlev W. Isotropy of quadratic spaces in finite and infinite dimension. Documenta mathematica, Tome 12 (2007), pp. 473-504. http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a7/