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
*Availability to be confirmed
[AGA23] Some participants at IMJ, Paris.
[AGA23] Participants at RIMS Kyoto.

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).