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Minimal forms wit respect to function fields of conics

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Summary

LetF be a field of characteristic ≠2, and let ϱ be an anisotropic conic overF. Anisotropic quadratic forms φ overF which become isotropic over the function fieldF(ϱ), but which do not contain proper subforms becoming isotropic, are calledF(ϱ)-minimal forms. It is investigated how upper bounds for the dimension ofF(ϱ)-minimal forms depend on certain properties and invariants of the fieldF. The existence of fieldsF and conics ϱ such thatF containsF(ϱ)-minimal forms of arbitrarily large (odd) dimension is proved.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, 40506-0027, Lexington, KY, USA

    D. W. Hoffmann

  2. Department of Pure Mathematics and Computer Algebras, University of Ghent, Galglaan 2, B-9000, Gent, Belgium

    J. Van Geel

Authors
  1. D. W. Hoffmann
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  2. J. Van Geel
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Additional information

During the work on this article, the first author was a postdoc at the Institute for Experimental Mathematics, University of Essen, Germany, supported by a grant from the Deutsche Forschungsgemeinschaft

This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.

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Hoffmann, D.W., Van Geel, J. Minimal forms wit respect to function fields of conics. Manuscripta Math 86, 23–48 (1995). https://doi.org/10.1007/BF02567976

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  • DOI: https://doi.org/10.1007/BF02567976

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