3-Cocycles, symbols and reciprocity laws on curves
[EN]We introduce a new approach for the study of two-dimensional symbols, F^∗ ×F^∗ ×F^∗ → G, where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{...
| Autor: | |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/164060 |
| Acceso en línea: | http://hdl.handle.net/10366/164060 |
| Access Level: | acceso abierto |
| Palabra clave: | 3-cocycle Arithmetic symbols Reciprocity laws 12 Matemáticas |
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3-Cocycles, symbols and reciprocity laws on curvesPablos Romo, Fernando3-cocycleArithmetic symbolsReciprocity laws12 Matemáticas[EN]We introduce a new approach for the study of two-dimensional symbols, F^∗ ×F^∗ ×F^∗ → G, where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{·, ·, ·}] ∈ H^3(F^∗,G). Our construction generalizes well-known two-dimensional symbols, such as the Parshin symbol on a surface, and we offer a proof and a conjecture for reciprocity laws on curves related to these symbols.Elsevier202520252006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10366/164060reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésBFM2003-00078SA071/04.info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1640602026-06-07T06:28:51Z |
| dc.title.none.fl_str_mv |
3-Cocycles, symbols and reciprocity laws on curves |
| title |
3-Cocycles, symbols and reciprocity laws on curves |
| spellingShingle |
3-Cocycles, symbols and reciprocity laws on curves Pablos Romo, Fernando 3-cocycle Arithmetic symbols Reciprocity laws 12 Matemáticas |
| title_short |
3-Cocycles, symbols and reciprocity laws on curves |
| title_full |
3-Cocycles, symbols and reciprocity laws on curves |
| title_fullStr |
3-Cocycles, symbols and reciprocity laws on curves |
| title_full_unstemmed |
3-Cocycles, symbols and reciprocity laws on curves |
| title_sort |
3-Cocycles, symbols and reciprocity laws on curves |
| dc.creator.none.fl_str_mv |
Pablos Romo, Fernando |
| author |
Pablos Romo, Fernando |
| author_facet |
Pablos Romo, Fernando |
| author_role |
author |
| dc.subject.none.fl_str_mv |
3-cocycle Arithmetic symbols Reciprocity laws 12 Matemáticas |
| topic |
3-cocycle Arithmetic symbols Reciprocity laws 12 Matemáticas |
| description |
[EN]We introduce a new approach for the study of two-dimensional symbols, F^∗ ×F^∗ ×F^∗ → G, where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{·, ·, ·}] ∈ H^3(F^∗,G). Our construction generalizes well-known two-dimensional symbols, such as the Parshin symbol on a surface, and we offer a proof and a conjecture for reciprocity laws on curves related to these symbols. |
| publishDate |
2006 |
| dc.date.none.fl_str_mv |
2006 2025 2025 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/10366/164060 |
| url |
http://hdl.handle.net/10366/164060 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
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BFM2003-00078 SA071/04. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier |
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Elsevier |
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reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca instname:Universidad de Salamanca (USAL) |
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Universidad de Salamanca (USAL) |
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GREDOS. Repositorio Institucional de la Universidad de Salamanca |
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GREDOS. Repositorio Institucional de la Universidad de Salamanca |
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1869416478149705728 |
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15.811543 |