Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ 2023
Local-global principles and the patching method
The patching method has a long history in inverse Galois theory going back to applications of Serre’s GAGA principle to algebraize complex patched coverings. Later, Harbater proved, by patching and gluing G-covers with totally K-rational fibers with K a complete valued field, the Regular Inverse Galois Problem for such fields in 1987 and the Abhyankar’s conjecture in 1984. More recently, this method has been brought to a new light by Harbater, Hartmann and Krashen with the development of patching techniques over function fields of algebraic curves over complete discretely valued fields.
The goal of the workshop is to give a practical understanding of the patching method and how it provides arithmetic results, we refer to the 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).
Next Atelier. Following the vote of the participants, the next atelier will be ``Around Grothendieck-Teichmüller group''.
List of participants
The Atelier takes place in-person with a Zoom bridge between RIMS Kyoto and Paris.
| Assoun Antonin | Université de Lille | Paris |
| Elyes Boughattas | Université Sorbonne Paris Nord | Paris |
| Elias Caeiro | École Normale Supérieure Paris | Paris |
| Melvyn El kamel-meyrigne | École Polytechnique (CMLS) | Paris |
| Mattias Ferreira-filoramo | Sorbonne Université | Paris |
| Keita Goto | Kyoto University | Kyoto |
| Oussama Hamza* | Western University CA | Paris |
| Tetsuya Ishida* | Saga university | Kyoto |
| Antoine Klughertz | Sorbonne Université | Paris |
| Joseph Leclere | Ecole Normale Supérieure de Paris | Paris |
| Louis Loiseau | Université de Nantes | Paris |
| Manh-Linh Nguyen | Université Paris-Saclay | Paris |
| Séverin Philip | RIMS Kyoto | Kyoto |
| Marceau Ringuedé | ENS Rennes | Kyoto |
| Owen Sabatin | École normale supérieur Paris | Paris |
| Xinyu Shao | IMJ-PRG | Paris |
| Densuke Shiraishi | Osaka University | Kyoto |
| Naganori Yamaguchi | Tokyo Institute of Technology | Kyoto |
| Anis Zidani* | Paris Saclay University | Paris |
Would you be interested in attending or giving a talk, please contact one of the organizers -- E. Boughattas (France), S. Philip (RIMS JP) or N. Yamaguchi (RIMS JP).