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 16, 2024 | Autumn in Paris 2024 - Four researchers of RIMS, Kyoto University visits ENS Paris and other AHGT French researchers , Sept. 16-Oct. 07, 2024 |
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Jul 19, 2024 | Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ - Spaces and perfectoids , July 19, 2024 |
AHGT Seminar
Jul 1, 2024 | On the reducibility of fibers of polynomials. Angelot Behajaina (Technion & Open University of Israel) |
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Jun 3, 2024 | Towards Uniform Finiteness Results on Heavenly Elliptic Curves. Christopher Rasmussen (Wesleyan University, USA) |
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.