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.

Speakers & participants (registration in progress...)

The Atelier takes place in a Zoom hybrid format between RIMS Kyoto and 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).