Isolated points on modular curves

Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al but finitely many algebraic points on a curve arise in families parametrized by $\mathbb{P}^{1}$ or positive rank abelian varieties, we call these finitely many exceptions isolated points. We study...

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Main Author: Viray, Bianca
Format: Article in Journal/Newspaper
Language:unknown
Published: CIRM 2019
Subjects:
11G05
11G18
11G30
Théorie des Nombres
ejder
Online Access:https://dx.doi.org/10.24350/cirm.v.19538003
https://library.cirm-math.fr/Record.htm?record=19286299124910044719
id ftdatacite:10.24350/cirm.v.19538003
record_format openpolar
spelling ftdatacite:10.24350/cirm.v.19538003 2023-05-15T16:04:54+02:00 Isolated points on modular curves Viray, Bianca 2019 MP4 https://dx.doi.org/10.24350/cirm.v.19538003 https://library.cirm-math.fr/Record.htm?record=19286299124910044719 unknown CIRM http://library.cirm-math.fr/19538003.vtt https://conferences.cirm-math.fr/1921.html CC BY NC ND https://creativecommons.org/licenses/by-nc-nd/4.0 CC-BY-NC-ND 11G05 11G18 11G30 Théorie des Nombres Audiovisual video conference article MediaObject 2019 ftdatacite https://doi.org/10.24350/cirm.v.19538003 2021-11-05T12:55:41Z Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al but finitely many algebraic points on a curve arise in families parametrized by $\mathbb{P}^{1}$ or positive rank abelian varieties, we call these finitely many exceptions isolated points. We study how isolated points behave under morphisms and then specialize to the case of modular curves. We show that isolated points on $X_{1}(n)$ push down to isolated points on aj only on the $j$-invariant of the isolated point. This is joint work with A. Bourdon, O. Ejder, Y. Liu, and F. Odumodu. Article in Journal/Newspaper ejder DataCite Metadata Store (German National Library of Science and Technology)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic 11G05
11G18
11G30
Théorie des Nombres
spellingShingle 11G05
11G18
11G30
Théorie des Nombres
Viray, Bianca
Isolated points on modular curves
topic_facet 11G05
11G18
11G30
Théorie des Nombres
description Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al but finitely many algebraic points on a curve arise in families parametrized by $\mathbb{P}^{1}$ or positive rank abelian varieties, we call these finitely many exceptions isolated points. We study how isolated points behave under morphisms and then specialize to the case of modular curves. We show that isolated points on $X_{1}(n)$ push down to isolated points on aj only on the $j$-invariant of the isolated point. This is joint work with A. Bourdon, O. Ejder, Y. Liu, and F. Odumodu.
format Article in Journal/Newspaper
author Viray, Bianca
author_facet Viray, Bianca
author_sort Viray, Bianca
title Isolated points on modular curves
title_short Isolated points on modular curves
title_full Isolated points on modular curves
title_fullStr Isolated points on modular curves
title_full_unstemmed Isolated points on modular curves
title_sort isolated points on modular curves
publisher CIRM
publishDate 2019
url https://dx.doi.org/10.24350/cirm.v.19538003
https://library.cirm-math.fr/Record.htm?record=19286299124910044719
genre ejder
genre_facet ejder
op_relation http://library.cirm-math.fr/19538003.vtt
https://conferences.cirm-math.fr/1921.html
op_rights CC BY NC ND
https://creativecommons.org/licenses/by-nc-nd/4.0
op_rightsnorm CC-BY-NC-ND
op_doi https://doi.org/10.24350/cirm.v.19538003
_version_ 1766400544224575488

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