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
Apr 1, 2025 | Workshop Arithmetic France-Japan - 日本 x フランス 数論幾何学 2025 , Apr14-18, 2025 |
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Dec 23, 2024 | B. Fresse (Lille) gives a one-semester advanced course on ``Operads, graph complexes and applications'' [Prog] , Jan.-Mar., 2025 |
AHGT Seminar
Feb 3, 2025 | Convolution groups of perverse sheaves on abelian varieties. Haohao Liu (IRMA Strasbourg, France) |
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Jan 6, 2025 | Recovering the combinatorial structure of a covering of schemes using glued Galois categories. Paul Helminck (Tohoku University (JSPS), Japan) |
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.