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Submission: 2011, Jun 16
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.
2010 Mathematics Subject Classification: 11E04, 11E10, 11E81, 12D15
Keywords and Phrases: quadratic form, real field, preordering, fan, Witt ring, powers of the fundamental ideal, real valuation, residue map, length, u-invariant, stability index, rational function field, power series field
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