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:
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(a) Isotropy of 7-dimensional forms and 8-dimensional forms.
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(b) Stable equivalence of 9-dimensional forms.
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(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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Online ISBN: 978-3-540-40990-8
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