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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188553 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Witt equivalence of function fields of conics / P. Gladki, M. Marshall // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 63–78. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862664713560653824 |
|---|---|
| author | Gladki, P. Marshall, M. |
| author_facet | Gladki, P. Marshall, M. |
| citation_txt | Witt equivalence of function fields of conics / P. Gladki, M. Marshall // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 63–78. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T15:15:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188553 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:15:19Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Gladki, P. Marshall, M. 2023-03-05T17:25:07Z 2023-03-05T17:25:07Z 2020 Witt equivalence of function fields of conics / P. Gladki, M. Marshall // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 63–78. — Бібліогр.: 20 назв. — англ. 1726-3255 DOI:10.12958/adm1271 2000 MSC: Primary 11E81, 12J20; Secondary 11E04, 11E12 https://nasplib.isofts.kiev.ua/handle/123456789/188553 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Witt equivalence of function fields of conics Article published earlier |
| spellingShingle | Witt equivalence of function fields of conics Gladki, P. Marshall, M. |
| title | 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_short | Witt equivalence of function fields of conics |
| title_sort | witt equivalence of function fields of conics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188553 |
| work_keys_str_mv | AT gladkip wittequivalenceoffunctionfieldsofconics AT marshallm wittequivalenceoffunctionfieldsofconics |