Introduction

The IEA ArGex (International Emerging Action Arithmetic and Galois extensions of function fields), managed by Dr. Tuan Ngo Dac (CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1) in collaboration with Dr. Nguyen Duy Tan (Institute of Mathematics, Vietnam Academy of Science and Technology) will be effective in 2020 and 2021.

Missions and research themes

This project concerns investigations in Number Theory. This is one of the fundamental branches of mathematics which has practical applications in computer science (e.g., in coding theory) and cryptography. The investigators propose several projects in arithmetic geometry and number theory that explore deep links between the analytic, arithmetic and combinatorial information encoded in certain objects associated to global function fields and their Galois extensions. Of particular interest, we focus on explicit construction of Galois extensions of function fields and on quantities attached to Anderson-Drinfeld motives, especially special zeta and L-values. We should mention that our proposal is suitable for numerical experiments as well as applications to cryptography or coding theory such as the construction of curves having many rational points. 
Keywords. Curves over a finite field, Drinfeld modules, Anderson motives, Galois cohomology, function field, Massey products, zeta and L-values, transcendence theory.

Main projects of research

Our proposal is composed of two main projects of research. The first one investigates several explicit construction of Galois extensions of function fields. The second one concerns function field arithmetic via combinatorial and transcendence methods.
17-28 Feb 2020
Organizers : Nguyen Duy Tan, Nguyen Chu Gia Vuong, Phung Ho Hai (IMH, Vietnam) Tuan Ngo Dac (CNRS Lyon 1, France) and Bruno Anglès (Caen, France),
CIMPA-SEAMS School “Arithmetic, Geometry and Model Theory”, Hanoi (Vietnam).

institutions and laboratories involved

France
• Dr. Tuan Ngo Dac (UMR5208, Institut Camille Jordan, CNRS and Université Claude Bernard, Lyon, head of the team)
• Bruno Anglès (Laboratoire de Mathématiques Nicolas Oresme, CNRS and Université de Caen)
• Tiphaine Beaumont (PhD student, Université de Caen)
• Huy Hung Le (PhD student, Université de Caen)

Vietnam
• Dr. Duy Tan Nguyen (Researcher, IMH Hanoi, local head)
• Chu Gia Vuong Nguyen (Researcher, IMH Hanoi)
• Lan Huong Pham (PhD student and researcher, IMH Hanoi)