Jeudi 26 mai 2016 à 15h00 en salle C48
Thomas Houtmann (Université de Caen)

Titre : The complex analytic CM method in genus 2 for non-maximal orders

Résumé :
In this talk, we will give several results on the complex multiplication (CM) method for genus 2 curves and several results on orders in primitive quartic CM number fields. The main result is a generalisation of the complex analytic CM method to arbitrary orders. The algorithm computes class polynomials whose root system are invariants of genus 2 curves with prescribed endomorphism ring. In the literature, the maximal order is mainly considered. In primitive quartic CM fields, we will propose the beginning of a complete description of orders, stable by complex conjugation. Those orders are "strong" candidates for endomorphism rings of genus 2 curves. We will recall how to build models for those curves.