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RESEARCH ARTICLE
Witt equivalence of function fields of conics
P. Gladkiab, M. Marshallab a Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland
b Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
Abstract:
Two fields are Witt equivalent if, roughly speaking, they have the same quadratic form theory. Formally, that is to say that their Witt rings of symmetric bilinear forms are isomorphic. This equivalence is well understood only in a few rather specific classes of fields. Two such classes, namely function fields over global fields and function fields of curves over local fields, were investigated by the authors in their earlier works [5] and [6]. In the present work, which can be viewed as a sequel to the earlier papers, we discuss the previously obtained results in the specific case of function fields of conic sections, and apply them to provide a few theorems of a somewhat quantitive flavour shedding some light on the question of numbers of Witt non-equivalent classes of such fields.
Keywords:
symmetric bilinear forms, quadratic forms, Witt equivalence of fields, function fields, conic sections, valuations, Abhyankar valuations.
Received: 25.10.2018
Citation:
P. Gladki, M. Marshall, “Witt equivalence of function fields of conics”, Algebra Discrete Math., 30:1 (2020), 63–78
Linking options:
https://www.mathnet.ru/eng/adm765 https://www.mathnet.ru/eng/adm/v30/i1/p63
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Abstract page: | 48 | Full-text PDF : | 31 | References: | 14 |
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