An l-adic CM construction for genus 2

We recall recent work on CM constructions using canonical lifts of the Frobenius isogeny: for p = 2 with Gaudry, Houtmann, Ritzenthaler, and Weng, and generalisation to p = 3 with Carls and Lubicz. I will explain how to extend this to (l,l)-isogenies for l = 2, 3 coprime to the characteristic.