james.oshea@maths.nuim.ie or james.oshea@ucd.ie

Submission: 2015, May 13

The isotropy of multiples of Pfister forms is studied. Some classical results are recalled and their consequences presented, with certain of these statements being hitherto unpublished. In particular, a lower bound on the first Witt index of Pfister multiples is established and a number of its corollaries are outlined. The relationship between a form and its Pfister multiples is explored, with particular attention being devoted to the case where the Pfister form is generic. Isotropy statements are obtained in this context, with related results demonstrating a strong correspondence between the properties of a form of those of its generic Pfister multiples. These correspondence results are applied to discriminate between properties inherited by Pfister multiples, with some novel examples being provided in this regard.

2010 Mathematics Subject Classification: 11E04, 11E10, 11E25, 11E81, 12F20

Keywords and Phrases: Quadratic forms, Pfister multiples, first Witt index, generic Pfister forms

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