Uniform bounds for the number of rational points on varieties over global fields

Autores
Paredes, Marcelo Exequiel; Sasyk, Roman
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.
Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; Argentina
Materia
DETERMINANT METHOD
HEIGHTS IN GLOBAL FIELDS
NUMBER OF RATIONAL SOLUTIONS OF DIOPHANTINE EQUATIONS
VARIETIES OVER GLOBAL FIELDS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/204676
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Uniform bounds for the number of rational points on varieties over global fieldsParedes, Marcelo ExequielSasyk, RomanDETERMINANT METHODHEIGHTS IN GLOBAL FIELDSNUMBER OF RATIONAL SOLUTIONS OF DIOPHANTINE EQUATIONSVARIETIES OVER GLOBAL FIELDShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; ArgentinaMathematical Sciences Publishers2022-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/204676Paredes, Marcelo Exequiel; Sasyk, Roman; Uniform bounds for the number of rational points on varieties over global fields; Mathematical Sciences Publishers; Algebra and Number Theory; 16; 8; 11-2022; 1941-20001937-0652CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://msp.org/ant/2022/16-8/ant-v16-n8-p07-s.pdfinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2101.12174info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:59:43Zoai:ri.conicet.gov.ar:11336/204676instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:59:43.412CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Uniform bounds for the number of rational points on varieties over global fields
title Uniform bounds for the number of rational points on varieties over global fields
spellingShingle Uniform bounds for the number of rational points on varieties over global fields
Paredes, Marcelo Exequiel
DETERMINANT METHOD
HEIGHTS IN GLOBAL FIELDS
NUMBER OF RATIONAL SOLUTIONS OF DIOPHANTINE EQUATIONS
VARIETIES OVER GLOBAL FIELDS
title_short Uniform bounds for the number of rational points on varieties over global fields
title_full Uniform bounds for the number of rational points on varieties over global fields
title_fullStr Uniform bounds for the number of rational points on varieties over global fields
title_full_unstemmed Uniform bounds for the number of rational points on varieties over global fields
title_sort Uniform bounds for the number of rational points on varieties over global fields
dc.creator.none.fl_str_mv Paredes, Marcelo Exequiel
Sasyk, Roman
author Paredes, Marcelo Exequiel
author_facet Paredes, Marcelo Exequiel
Sasyk, Roman
author_role author
author2 Sasyk, Roman
author2_role author
dc.subject.none.fl_str_mv DETERMINANT METHOD
HEIGHTS IN GLOBAL FIELDS
NUMBER OF RATIONAL SOLUTIONS OF DIOPHANTINE EQUATIONS
VARIETIES OVER GLOBAL FIELDS
topic DETERMINANT METHOD
HEIGHTS IN GLOBAL FIELDS
NUMBER OF RATIONAL SOLUTIONS OF DIOPHANTINE EQUATIONS
VARIETIES OVER GLOBAL FIELDS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.
Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; Argentina
description We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.
publishDate 2022
dc.date.none.fl_str_mv 2022-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/204676
Paredes, Marcelo Exequiel; Sasyk, Roman; Uniform bounds for the number of rational points on varieties over global fields; Mathematical Sciences Publishers; Algebra and Number Theory; 16; 8; 11-2022; 1941-2000
1937-0652
CONICET Digital
CONICET
url http://hdl.handle.net/11336/204676
identifier_str_mv Paredes, Marcelo Exequiel; Sasyk, Roman; Uniform bounds for the number of rational points on varieties over global fields; Mathematical Sciences Publishers; Algebra and Number Theory; 16; 8; 11-2022; 1941-2000
1937-0652
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://msp.org/ant/2022/16-8/ant-v16-n8-p07-s.pdf
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2101.12174
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Mathematical Sciences Publishers
publisher.none.fl_str_mv Mathematical Sciences Publishers
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613769330688000
score 13.070432

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