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.
AHGT News & Activities
| Apr 1, 2025 | Workshop Arithmetic France-Japan - 日本 x フランス 数論幾何学 2025 , Apr 14 - 18, 2025 |
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| Mar 25, 2025 | Low dimensional topology and number theory XVI: In honor of Professor Hiroaki Nakamura's 60th birthday , March 25 - 28, 2025 |
AHGT Seminar
| Jul 7, 2025 | Automorphism groups of field extensions and the minimal ramification problem. Alexei Entin (Tel-Aviv University, Israel) |
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| Jun 16, 2025 | When small points have their good reasons. Sara Checcoli (Institut Fourier Grenoble, France) |
Research Topics
The scientific activity of the AHGT IRN is structured around the 3 following topics and their interactions:
AHGT references
- Surveys & lectures notes, for a first contact with AHGT;
- Publications & preprints, per year and topic;
- ``Atelier Géométrie Arithmetic'' (notes), report on the young researches seminar.
- 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 [2024]:: [2023];
- 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 [2024]:: [2023];
- 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 [2024]:: [2023];
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
