Witt equivalence of function fields of conics
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 func...
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| Дата: | 2020 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1271 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-12712021-01-04T08:50:14Z Witt equivalence of function fields of conics Gladki, P. Marshall, M. symmetric bilinear forms, quadratic forms, Witt equivalence of fields, function fields, conic sections, valuations, Abhyankar valuations Primary 11E81, 12J20; Secondary 11E04, 11E12 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. Lugansk National Taras Shevchenko University 2020-12-30 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1271 10.12958/adm1271 Algebra and Discrete Mathematics; Vol 30, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1271/pdf Copyright (c) 2020 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2021-01-04T08:50:14Z |
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OJS |
| language |
English |
| topic |
symmetric bilinear forms quadratic forms Witt equivalence of fields function fields conic sections valuations Abhyankar valuations Primary 11E81 12J20; Secondary 11E04 11E12 |
| spellingShingle |
symmetric bilinear forms quadratic forms Witt equivalence of fields function fields conic sections valuations Abhyankar valuations Primary 11E81 12J20; Secondary 11E04 11E12 Gladki, P. Marshall, M. Witt equivalence of function fields of conics |
| topic_facet |
symmetric bilinear forms quadratic forms Witt equivalence of fields function fields conic sections valuations Abhyankar valuations Primary 11E81 12J20; Secondary 11E04 11E12 |
| format |
Article |
| author |
Gladki, P. Marshall, M. |
| author_facet |
Gladki, P. Marshall, M. |
| author_sort |
Gladki, P. |
| title |
Witt equivalence of function fields of conics |
| title_short |
Witt equivalence of function fields of conics |
| title_full |
Witt equivalence of function fields of conics |
| title_fullStr |
Witt equivalence of function fields of conics |
| title_full_unstemmed |
Witt equivalence of function fields of conics |
| title_sort |
witt equivalence of function fields of conics |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1271 |
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AT gladkip wittequivalenceoffunctionfieldsofconics AT marshallm wittequivalenceoffunctionfieldsofconics |
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2025-12-02T15:44:05Z |
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2025-12-02T15:44:05Z |
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