Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

Collection Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

Organizer(s) Anni, Samuele ; Karemaker, Valentijn ; Lorenzo Garcia, Elisa

Date(s) 31/05/2021 - 04/06/2021

linked URL https://conferences.cirm-math.fr/2558.html

00:00:00 / 00:00:00

5 18

Maps between curves and diophantine obstructions

By José Felipe Voloch

Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise.

Information about the video

Date of recording 20/06/2017
Date of publication 29/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19186203
Cite this video Voloch, José Felipe (20/06/2017). Maps between curves and diophantine obstructions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19186203
URL https://dx.doi.org/10.24350/CIRM.V.19186203

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