Dimensions of Anisotropic Indefinite Quadratic Forms II

  • Detlev W. Hoffmann


The uu-invariant and the Hasse number u~\tilde u of a field FF of characteristic not 2 are classical and important field invariants pertaining to quadratic forms. They measure the suprema of dimensions of anisotropic forms over FF that satisfy certain additional properties. We prove new relations between these invariants and a new characterization of fields with finite Hasse number (resp. finite uu-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.