Geodesic
Isotropy of quadratic spaces in finite and infinite dimension
Documenta mathematica, Tome 12 (2007), pp. 473-504
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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.
DOI : 10.4171/dm/231
Classification : 11E04, 11E81, 12D15, 12E15, 12F20, 12G05, 12G10, 16K20, 19D45
Mots-clés : cohomological dimension, quadratic form, Galois cohomology, isotropy, infinite-dimensional quadratic space, u-invariant, function field of a quadric, totally indefinite form, real field, division algebra, quaternion algebra, symbol algebra, Milnor K-theory 
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     author = {Karim Johannes Becher and Detlev W. Hoffmann},
     title = {Isotropy of quadratic spaces in finite and infinite dimension},
     journal = {Documenta mathematica},
     pages = {473--504},
     year = {2007},
     volume = {12},
     doi = {10.4171/dm/231},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/231/}
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Karim Johannes Becher; Detlev W. Hoffmann. Isotropy of quadratic spaces in finite and infinite dimension. Documenta mathematica, Tome 12 (2007), pp. 473-504. doi: 10.4171/dm/231

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