Felipe Voloch: Maps between curves and diophantine obstructions

Abstract: 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.

Recording during the thematic meeting : "Arithmetic, Geometry, Cryptography and Coding Theory" the June 20, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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