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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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188553 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
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dspace |
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irk-123456789-1885532023-03-06T01:27:07Z Witt equivalence of function fields of conics Gladki, P. Marshall, M. 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. 2020 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/188553 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Gladki, P. Marshall, M. |
| spellingShingle |
Gladki, P. Marshall, M. Witt equivalence of function fields of conics Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188553 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT gladkip wittequivalenceoffunctionfieldsofconics AT marshallm wittequivalenceoffunctionfieldsofconics |
| first_indexed |
2023-10-18T23:08:37Z |
| last_indexed |
2023-10-18T23:08:37Z |
| _version_ |
1796157360315564032 |