Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ 2024
Spaces and perfectoids towards a perfectoid Siegel modular space
The notion of a perfectoid space was introduced by Scholze in 2012. It readily had a plethora of strong applications such as in p-adic Hodge theory and the Langlands program. To quote Bhatt in 2014, “The theory of perfectoid spaces is rather young, but already extremely potent: each class of examples discovered so far has led to powerful and deep theorems in arithmetic geometry”.
The inspiration of perfectoid spaces come from the reunion of a classical result of Fontaine and Wintenberger in Galois theory, the theories of analytic geometry over non-archimedean spaces
as given by Huber adic spaces, Berkovich spaces and the rigid-analytic geometry of Tate, and
Faltings “almost mathematics” developped by Gaber and Ramero.
The goal of the workshop is to provide an introduction to the theory of perfectoid spaces and see it in application with the construction of a Siegel perfectoid space and a Hodge-Tate period map following Scholze. The classical GIT-construction of a fine moduli space for abelian varieties with level structure will be presented. See program for a description of talks and a list of references.
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 de Paris | Paris |
| Simon Alonso | École Normale Supérieure de Lyon | Paris |
| Antonin Assoun | Université de Lille | Paris |
| Justin Carel | École normale supérieure de Paris | Paris |
| Caeiro Elias | École Normale Supérieure | Paris |
| Nino Emery | École Normale Supérieure de Lyon | Paris |
| Tokihiro Fushimi | RIMS Kyoto University | Kyoto |
| Felipe Gambardella | École Polytechnique | Paris |
| Paul Alexander Helminck | Tohoku University | Kyoto |
| Ryo Ishizuka | Tokyo Institute of Technology | Kyoto |
| Ito Kashu | Ritsumeikan University | Kyoto |
| Akasaka Keima | Chiba University | Kyoto |
| Alexander Kenigswald | ENS de Lyon | Paris |
| Antoine Klughertz | École Normale Supérieure de Lyon | Paris |
| Kaiji Kondo | RIMS Kyoto University | Kyoto |
| Brieuc Lair | École normale supérieure de Paris | Paris |
| Loiseau Louis | Université de Bordeaux | Paris |
| Kenza Memlouk | École Normale Supérieure de Lyon | Paris |
| Enguerrand Moulinier | Sorbonne University | Paris |
| Séverin Philip | RIMS Kyoto University | Kyoto |
| Lucas Hiroyuki Ragni hamada | Tokyo Institute of Technology | Kyoto |
| Kazuki Sekine | Institute of Information Security | Kyoto |
| Taisei Shin | RIMS Kyoto University | Kyoto |
| Matteo Soreda | ENS Rennes | Kyoto |
| Reiya Tachihara | RIMS Kyoto University | Kyoto |
| Naoka Takada | Osaka University | Kyoto |
| Naganori Yamaguchi | Tokyo Institute of Technology | Kyoto |
| Hsin-Yi Yang | Utrecht University | Paris |
| Kexuan Yang | University of North Carolina at Chapel Hill | Kyoto |
| Adrien Zabat | Sorbonne University | Paris |
The Atelier takes place in-person* with a Zoom bridge between RIMS Kyoto and Paris. Participants proposes and vote for the next Atelier topic.
.png "[AGA24] Group picture at IMJ Paris (online)")
Organizers: Ferreira-Filoramo (France), Philip (RIMS Japan), Takada (Osaka Japan) or Yamaguchi (Tokyo Japan).
* Due to the Paris Olympic Games 2024 and Security measure, there is no access to ENS or to Jussieu, see [Map;Resource].