Submission: 2010 Sep 10
The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the isotropy question is explored. Moreover, in the case where the ground field is formally real and has finite Hasse number, the isotropy question is answered for forms of sufficiently large dimension.
2000 Mathematics Subject Classification: 11E04, 11E10, 11E81
Keywords and Phrases: Function fields of quadratic forms, Pfister forms, minimal forms, excellence, Hasse number
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