On smooth plane models for modular curves of Shimura type | Vidéo | Carmin.tv

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On smooth plane models for modular curves of Shimura type

By Elisa Lorenzo García

Appears in collection : COUNT - Computations and their Uses in Number Theory / Les calculs et leurs utilisations en théorie des nombres

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.

Information about the video

Date of recording 2/27/23
Date of publication 3/13/23
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20007003
Cite this video Lorenzo García Elisa (2/27/23). On smooth plane models for modular curves of Shimura type. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20007003
URL https://dx.doi.org/10.24350/CIRM.V.20007003

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Bibliography

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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