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
Sep 28, 2024 | Oberwolfach workshop - Anabelian Geometry & Representations of Fundamental Groups., Sep.29 - Oct.4, 2024 |
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Sep 23, 2024 | Workshop ``AHGT Days in Paris 2024'' , Sept. 23-24, 2024 |
AHGT Seminar
Oct 21, 2024 | On the geometric outer monodromy representation and the Grothendieck conjecture of hyperbolic curves. IIJIMA Yu (Hiroshima University, Japan) |
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Sep 2, 2024 | p-adic L-function: survey + epsilon. OCHIAI Tadashi (Tokyo Institute of Technology) |
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.