Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ 2025
Étale homotopy theory and application
Étale homotopy theory of schemes, then Friedlander's refinement the étale topological type, introduced by M. Artin and B. Mazur in the 60s, is an analogue in algebraic geometry of classical homotopy theory for topological spaces.
A promising application of étale homotopy theory was initiated by Schmidt-Stix, with the result that smooth schemes, including in higher dimension, admit a fundamental system of Zariski neighbourhoods that are anabelian*.
With the aim of presenting anabelian geometry through the lens of étale topology types, we will study the main constructions of the étale topological type and tools of étale homotopy theory with illustrative examples; we will also cover the definition of the étale homotopy groups. We refer to program for a description of talks and a list of references.
* A similar result was obtained by Y.Hoshi with different techniques.
This atelier is organized with the support of the École Parisienne d'Arithmétique et de Géométrie (ÉPAG).
List of participants
| Matthias Alizon | École normale supérieure | Paris |
| Justin Carel | ENS PSL | Paris |
| Lucas Dauger | Sorbonne university | Paris |
| Mattias Ferreira-filoramo | Sorbonne university | Paris |
| Jules Fressonnet | ENS PSL | Paris |
| Antoine Galet | Sorbonne university | Paris |
| Felipe Gambardella | École Polytechnique | Paris |
| Alexandre Kenigswald | Ens de Lyon - Laboratoire d'Orsay | Paris |
| Kaiji Kondo | RIMS Kyoto University | Kyoto |
| Yi Kung | University of Tokyo | Kyoto |
| Brieuc Lair | Institut de mathématiques de Bordeaux | Paris |
| Louis Loiseau | -- | Paris |
| Enguerrand Moulinier | Université Marie et Louis Pasteur | Paris |
| Karube Naoka | Osaka university | Kyoto |
| Lucas Perryman-deskins | Oregon State University | Kyoto |
| Drimik Roy-chowdhury | IMJ-PRG | Paris |
| Taisei Shin | RIMS Kyoto University | Kyoto |
| Naganori Yamaguchi | Institute of Science Tokyo | Kyoto |
| 和貴 馬杉 | RIMS Kyoto University | Kyoto |
The Atelier takes place in-person* with a Zoom bridge between RIMS Kyoto and Paris. Participants proposes and vote for the next Atelier topic.
Organizers: Ferreira-Filoramo (Sorbonne University, France), Galet (Sorbonne University, France) and Yamaguchi (Institute of Science Tokyo, Japan).