Isolated points on modular curves

Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al butfinitely many algebraic points on a curve arise in families parametrized byP1or positive rank abelian va-rieties; we call these finitely many exceptions isolated points. We study how isolated po...

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Bibliographic Details
Main Author: Viray, Bianca
Format: Article in Journal/Newspaper
Language:English
Published: Centre International de Rencontres Mathématiques (CIRM) 2019
Subjects:
Mathematics
FOS Mathematics
Lachaud, Gilles
Gilles Lachaud
ejder
Online Access:https://dx.doi.org/10.5446/53532
https://av.tib.eu/media/53532
id ftdatacite:10.5446/53532
record_format openpolar
spelling ftdatacite:10.5446/53532 2023-05-15T16:04:54+02:00 Isolated points on modular curves Viray, Bianca 2019 https://dx.doi.org/10.5446/53532 https://av.tib.eu/media/53532 en eng Centre International de Rencontres Mathématiques (CIRM) Mathematics FOS Mathematics Lachaud, Gilles Gilles Lachaud Conference/Talk MediaObject article Audiovisual 2019 ftdatacite https://doi.org/10.5446/53532 2021-11-05T12:55:41Z Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al butfinitely many algebraic points on a curve arise in families parametrized byP1or positive rank abelian va-rieties; we call these finitely many exceptions isolated points. We study how isolated points behave undermorphisms and then specialize to the case of modular curves. We show that isolated points onX1(n) pushdown to isolated points on a modular curve whose level is bounded by a constant that depends only on thej-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 English
topic Mathematics
FOS Mathematics
Lachaud, Gilles
Gilles Lachaud
spellingShingle Mathematics
FOS Mathematics
Lachaud, Gilles
Gilles Lachaud
Viray, Bianca
Isolated points on modular curves
topic_facet Mathematics
FOS Mathematics
Lachaud, Gilles
Gilles Lachaud
description Faltings’s theorem on rational points on subvarieties of abelian varieties can be used to show that al butfinitely many algebraic points on a curve arise in families parametrized byP1or positive rank abelian va-rieties; we call these finitely many exceptions isolated points. We study how isolated points behave undermorphisms and then specialize to the case of modular curves. We show that isolated points onX1(n) pushdown to isolated points on a modular curve whose level is bounded by a constant that depends only on thej-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 Centre International de Rencontres Mathématiques (CIRM)
publishDate 2019
url https://dx.doi.org/10.5446/53532
https://av.tib.eu/media/53532
genre ejder
genre_facet ejder
op_doi https://doi.org/10.5446/53532
_version_ 1766400544380813312

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