Linear nested Artin approximation theorem for algebraic power series

We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of t...

Descripción completa

Detalles Bibliográficos
Autores: Castro Jiménez, Francisco Jesús, Popescu, Dorin, Rond, Guillaume
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/74461
Acceso en línea:https://hdl.handle.net/11441/74461
https://doi.org/10.1007/s00229-018-1025-0
Access Level:acceso abierto
Palabra clave:Henselian rings
Algebraic power series rings
Nested Artin approximation property
id ES_4f66377f1243d1bc5bba30f01f2fdd2e
oai_identifier_str oai:idus.us.es:11441/74461
network_acronym_str ES
network_name_str España
repository_id_str
spelling Linear nested Artin approximation theorem for algebraic power seriesCastro Jiménez, Francisco JesúsPopescu, DorinRond, GuillaumeHenselian ringsAlgebraic power series ringsNested Artin approximation propertyWe give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested approximation problem are equivalent.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalRomanian National Authority for Scientific ResearchANR (Agence nationale de la recherche) Projects STAAVFSpringerÁlgebraFQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/74461https://doi.org/10.1007/s00229-018-1025-0reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésManuscripta mathematica, 1-19.MTM2013-40455-PID-PCE-2011-1023ANR-2011 BS01 009ANR-12-JS01-0002-01https://link.springer.com/content/pdf/10.1007%2Fs00229-018-1025-0.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/744612026-06-17T12:51:07Z
dc.title.none.fl_str_mv Linear nested Artin approximation theorem for algebraic power series
title Linear nested Artin approximation theorem for algebraic power series
spellingShingle Linear nested Artin approximation theorem for algebraic power series
Castro Jiménez, Francisco Jesús
Henselian rings
Algebraic power series rings
Nested Artin approximation property
title_short Linear nested Artin approximation theorem for algebraic power series
title_full Linear nested Artin approximation theorem for algebraic power series
title_fullStr Linear nested Artin approximation theorem for algebraic power series
title_full_unstemmed Linear nested Artin approximation theorem for algebraic power series
title_sort Linear nested Artin approximation theorem for algebraic power series
dc.creator.none.fl_str_mv Castro Jiménez, Francisco Jesús
Popescu, Dorin
Rond, Guillaume
author Castro Jiménez, Francisco Jesús
author_facet Castro Jiménez, Francisco Jesús
Popescu, Dorin
Rond, Guillaume
author_role author
author2 Popescu, Dorin
Rond, Guillaume
author2_role author
author
dc.contributor.none.fl_str_mv Álgebra
FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
dc.subject.none.fl_str_mv Henselian rings
Algebraic power series rings
Nested Artin approximation property
topic Henselian rings
Algebraic power series rings
Nested Artin approximation property
description We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested approximation problem are equivalent.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/74461
https://doi.org/10.1007/s00229-018-1025-0
url https://hdl.handle.net/11441/74461
https://doi.org/10.1007/s00229-018-1025-0
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Manuscripta mathematica, 1-19.
MTM2013-40455-P
ID-PCE-2011-1023
ANR-2011 BS01 009
ANR-12-JS01-0002-01
https://link.springer.com/content/pdf/10.1007%2Fs00229-018-1025-0.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407817327181824
score 15.301629

Similares en LA Referencia