Karim Johannes Becher and Mélanie Raczek: Ramification sequences and Bezoutian forms

karimjohannes.becher@uantwerpen.be, melanie.raczek@uantwerpen.be

Submission: 2016, Feb 4, revised: 2016, Oct 21

We continue our study from [K.J. Becher, M. Raczek. On the second K-group of a rational function field. Pacific J. Math. 262 (2013): 1-9.] on the problem of bounding the number of symbols needed to obtain an element of the second K-group of a rational function field with given ramification. Here we focus on the case of Milnor K-groups modulo 2 for fields of characteristic different from 2. To a given ramification sequence, we associate a quadratic form defined over the base field and study its properties. In particular, we relate the Witt index of the quadratic form to the minimal number of symbols necessary to represent the ramification sequence.

2010 Mathematics Subject Classification: 12E30, 12G05, 12Y05, 19D45

Keywords and Phrases: Milnor K-theory, quadratic form, valuation, ramification

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