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Real fields, valuations, and quadratic forms

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Abstract

We study several field invariants arising in quadratic form theory. Some of the invariants considered are of particular interest in the study of real fields, including the length, the u-invariant, and the (reduced) stability index. In this context we give a systematic account of valuation theoretic arguments that lead to lower bounds for these invariants.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Universiteit Antwerpen, Middelheimcampus G, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Karim Johannes Becher

  2. Zukunftskolleg, Universität Konstanz, 78457, Konstanz, Germany

    Karim Johannes Becher

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

    David B. Leep

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  1. Karim Johannes Becher
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  2. David B. Leep
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Correspondence to Karim Johannes Becher.

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Becher, K.J., Leep, D.B. Real fields, valuations, and quadratic forms. manuscripta math. 141, 737–754 (2013). https://doi.org/10.1007/s00229-012-0597-3

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  • DOI: https://doi.org/10.1007/s00229-012-0597-3

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