English
On smooth plane models for modular curves of Shimura type
Multi angle
Auteurs : Lorenzo Garcia, Elisa (Auteur de la Conférence)
CIRM (Editeur )
11F11 - Holomorphic modular forms of integral weight
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14H45 - Special curves and curves of low genus
CIRM (Editeur )
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Résumé :
In this talk we will see that there are only finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater than or equal to 19, no such curve exists. For modular curves of Shimura type we will show that none can admit a smooth plane model of degree 5, 6 or 7. Further, if a modular curve of Shimura type admits a smooth plane model of degree 8 we will see that it must be a twist of one of four curves.
This is joint work with Samuele Anni and Eran Assaf.
Keywords : modular curves; congruence subgroups; cusp forms; canonical model
Codes MSC : This is joint work with Samuele Anni and Eran Assaf.
Keywords : modular curves; congruence subgroups; cusp forms; canonical model
11F11 - Holomorphic modular forms of integral weight
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
14H45 - Special curves and curves of low genus
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 13/03/2023 Date de captation : 27/02/2023 Sous collection : Research talks arXiv category : Number Theory ; Algebraic Geometry Domaine : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:00:50 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-27_Lorenzo-Garcia.mp4 
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Informations sur la Rencontre
Nom de la rencontre : COUNT - Computations and their Uses in Number Theory / Les calculs et leurs utilisations en théorie des nombresOrganisateurs de la rencontre : Anni, Samuele ; Allombert, Bill ; Balakrishnan, Jennifer ; Bruin, Peter ; Kilicer, Pinar ; Streng, Marco Dates : 27/02/2023 - 03/03/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2805.html
Données de citation
DOI : 10.24350/CIRM.V.20007003Citer cette vidéo: Lorenzo Garcia, Elisa (2023). On smooth plane models for modular curves of Shimura type. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20007003 URI : http://dx.doi.org/10.24350/CIRM.V.20007003 |
Voir aussi
- [Multi angle] Modular curves and finite groups: building connections via computation / Auteur de la Conférence Roe, David.
- [Multi angle] Endomorphism algebras of geometrically split abelian surfaces over Q / Auteur de la Conférence Guitart, Xavier.
- [Multi angle] Endomorphism algebras of geometrically split genus 2 jacobians over Q / Auteur de la Conférence Fité, Francesc.
- [Multi angle] Minimal torsion curves in geometric isogeny classes / Auteur de la Conférence Bourdon, Abbey.
Bibliographie
- ANNI, Samuele, ASSAF, Eran, et GARCÍA, Elisa Lorenzo. On smooth plane models for modular curves of Shimura type. arXiv preprint arXiv:2203.06370, 2022. - https://doi.org/10.48550/arXiv.2203.06370
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