Arithmetic, Geometry, Cryptography and Coding Theory

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. This volume contains the proceedings of the 19th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T), held from June 5 to June 9, 2023, at the Centre International de Rencontres Mathematiques in Luminy (Marseille, France). The conference brought together researchers at the interface of arithmetic and algebraic geometry with computer science and information theory including, in particular, applications to cryptography and error correcting codes. The articles in this volume are based on talks given at the conference. They represent a broad spectrum of research ranging from abstract theory to explicit algorithms, with the majority of articles devoted to curves and abelian varieties over finite fields, their isogenies, and their endomorphisms.