# Arithmetic & Homotopic Galois Theory

The LPP-RIMS Arithmetic & Homotopic Galois Theory IRN (AHGT) is a CNRS France-Japan International Research Network between Lille University (Laboratoire de Mathématiques Paul Painlevé), École Normale Supérieure - PSL (Département de Mathématiques et Applications), and the Research Institute for Mathematical Sciences, Kyoto University.

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## AHGT News

Jan 5, 2023 Séverin Philip (RIMS Kyoto) at the Séminaire Arithmétique of LPP Lille University, Lille University, January 5, 2023 Ariane Mézard (ENS PSL) visits RIMS, Kyoto University, December 18, 2022 to January 18, 2023

## AHGT Seminar

Dec 26, 2022 Deformations of p-adic Galois representations. Ariane Mézard (DMA, ENS Paris, France)
For schedule and more, see the page of the AHGT seminar.

## Research Topics

The scientific activity of the AHGT IRN is structured around the 3 following topics and their interactions:

• Galois Covers and Moduli Spaces. On the arithmetic of Hurwitz spaces, and Noether's program -- that originate in the Inverse Galois Problem -- and on Ihara's program that draw a bridge between number theory, motivic theory, and anabelian geometry [References];
• Motivic & Geometric Galois Representations. Étale cohomology theory, Galois Representations theory, and Perverse sheaves theory are fully integrated and bring their complementary techniques with a richer derived spectrum [References];
• Arithmetic Anabelian Geometry. Beyond Grothendieck's anabelian reconstruction program (and the section vs rational point issue), includes new minimality or close-to-anabelian'', and combinatorial arithmetic geometry approaches for new connections with Hurwitz spaces and Grothendieck-Teichmüller theory [References].

We refer to a selection of surveys of the fields and recent publications.

## Members & Research Partners

The network regroups the activity of around 60 researchers in France and in Japan, and is supported by 40 international researchers over 12 countries and 32 institutions.

## Institutional Partners*

*official finalization of the agreement in progress.
Coordinators: B. Collas° (RIMS, JP), Y. Hoshi (RIMS, JP), B. Fresse (Lille, FR), A. Mézard (ENS, FR).
Sponsors: P. Dèbes (Lille, FR) & A. Tamagawa (RIMS, JP)
°Indicates main coordinator.