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.
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].
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.