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 [{...

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Detalles Bibliográficos
Autor: Pablos Romo, Fernando
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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spelling 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
format article
status_str 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
dc.relation.none.fl_str_mv BFM2003-00078
SA071/04.
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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