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 (registration in progress...)
Please fill in the following registration form before August 15. 2025.
The Atelier takes place in-person* with a Zoom bridge between RIMS Kyoto and Paris. Participants proposes and vote for the next Atelier topic.
For question, feel free to contact one of the organizers Ferreira-Filoramo (Sorbonne University, France), Galet (Sorbonne University, France) or Yamaguchi (Institute of Science Tokyo, Japan).