Isotropy over function fields of Pfister forms

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Title: Isotropy over function fields of Pfister forms
Authors: O'Shea, James
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Date: 1-Jul-2012
Abstract: 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.
Funding Details: Irish Research Council for Science, Engineering and Technology
European Research Council
Type of material: Journal Article
Publisher: Elsevier
Copyright (published version): 2012 Elsevier Inc.
Keywords: Function fields of quadratic formsPfister formsMinimal-isotropy formsExcellenceHasse number
Subject LCSH: Forms, Quadratic
Forms, Pfister
DOI: 10.1016/j.jalgebra.2012.03.025
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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