Geodesic
Dimensions of anisotropic indefinite quadratic forms. II.
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 251-265.

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

The $u$-invariant and the Hasse number $\tilde u$ of a field $F$ of characteristic not 2 are classical and important field invariants pertaining to quadratic forms. They measure the suprema of dimensions of anisotropic forms over $F$ that satisfy certain additional properties. We prove new relations between these invariants and a new characterization of fields with finite Hasse number (resp. finite $u$-invariant for nonreal fields), the first one of its kind that uses intrinsic properties of quadratic forms and which, conjecturally, allows an `algebro-geometric' characterization of fields with finite Hasse number.
Classification : 11E04, 11E10, 11E81, 12D15, 14C25
Keywords: Pfister neighbor, formally real field, $u$-invariant, Hasse number, Pythagoras number, Rost projector 
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     author = {Hoffmann, Detlev W.},
     title = {Dimensions of anisotropic indefinite quadratic forms. {II.}},
     journal = {Documenta mathematica},
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     volume = {Andrei A. Suslin's Sixtieth Birthday},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a13/}
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Hoffmann, Detlev W. Dimensions of anisotropic indefinite quadratic forms. II.. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 251-265. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a13/