# Aurelien Sagnier (Paris): Connes-Consani's arithmetic sites for number fields with narrow class number one

Aurelien Sagnier, Ecole Polytechnique (Palaiseau, France), will give a talk with title: Connes-Consani's arithmetic sites for number fields with narrow class number one

Abstract: In this lecture, I will explain in the first part my understanding of the ideas that lead A. Connes and C. Consani to the construction of their arithmetic site for $\mathbb{Q}$. In the second part of the lecture, I will explain how I generalised A. Connes and C. Consani's contruction to number fields with narrow class number one, I will in particular illustrate of it works on the cases of $\mathbb{Q}(\imath)$ and $\mathbb{Q}(\sqrt{2})$.