Proceedings from the 19th AGC2T in Marseille merge theories and algorithms across arithmetic, algebraic geometry, cryptography, and coding. Focus is on curves, abelian varieties over finite fields, and their isogenies and endomorphisms, linking pure research with computational applications in information theory.

Yves Aubry, Fabien Herbaut, and Julien Monaldi, Closed points on curves over finite fields; Stephane Ballet, Alexis Bonnecaze, and Bastien Pacifico, Multiplication in finite fields with Chudnovsky-type algorithms over the projective line; Jean-Marc Couveignes and Jean Gasnier, Explicit Riemann-Roch spaces in the Hilbert class field; Kiran S. Kedlaya, The relative class number one problem for function fields, II; Harun Kir, The refined Humbert invariant for an automorphism group of a genus 2 curve; M. Koutchoukali, On the coefficients of the zeta-function's L-polynomial for algebraic function fields over finite fields; Dimitri Koshelev, Generation of two ""independent"" points on an elliptic curve of j-invariant \neq 0,1728; Sergey Rybakov, Principal polarization on products of abelian varieties over finite fields; Yuri G. Zarhin, Superelliptic Jacobians and central simple representations