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Some New Results Concerning Isotropy of Low-dimensional Forms

List of Examples and Results (Without Proofs)

Part of the Lecture Notes in Mathematics book series (LNM,volume 1835)

Abstract

Let ø and ψ be quadratic forms over a field F of characteristic ≠2. We give an (almost) complete classification of pairs ø, ψ of dimension ≤ 9 such that ø is stably equivalent to ψ. We also study the question when the form ø is isotropic over the function field of ψ. In the case where dim #x00F8; = 9 and dim ψ ≥ 9 we solve this problem completely.

The current draft contains only a list of results. We are planning to write three articles with the following titles:

  • (a) Isotropy of 7-dimensional forms and 8-dimensional forms.

  • (b) Stable equivalence of 9-dimensional forms.

  • (c) Isotropy of 10- and 12-dimensional forms.

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© 2004 Springer-Verlag

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Izhboldin, O.T. (2004). Some New Results Concerning Isotropy of Low-dimensional Forms. In: Tignol, JP. (eds) Geometric Methods in the Algebraic Theory of Quadratic Forms. Lecture Notes in Mathematics, vol 1835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40990-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-40990-8_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20728-3

  • Online ISBN: 978-3-540-40990-8

  • eBook Packages: Springer Book Archive