Witt equivalence of function fields of conics
| Autor: | Murray Marshall, Paweł Gładki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Conic section Quadratic form Rings and Algebras (math.RA) FOS: Mathematics Discrete Mathematics and Combinatorics Primary 11E81 12J20 Secondary 11E04 11E12 Function (mathematics) Mathematics - Rings and Algebras Bilinear form Equivalence (measure theory) Mathematics |
| Popis: | 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. 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. arXiv admin note: text overlap with arXiv:1601.08085 |
| Databáze: | OpenAIRE |
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