Pre-school on Basic Number Theory (Preparation for Summer School on Galois Representations and Reciprocity)
Thời gian: 08:00 đến 17:00 ngày 05/05/2024, 08:00 đến 17:00 ngày 07/05/2024, 08:00 đến 17:00 ngày 12/05/2024, 08:00 đến 17:00 ngày 14/05/2024, 08:00 đến 17:00 ngày 19/05/2024, 08:00 đến 17:00 ngày 21/05/2024, 08:00 đến 17:00 ngày 26/05/2024,
Địa điểm: VIASM
Objectives: A pre-school series of lectures on selected topics in Galois cohomology, modular forms, and class field theory will be organized to prepare the participants for the main topics of the summer school.
Learning mode: Hybrid (Offline at VIASM and Online via Zoom)
Registration: If you wish to attend the pre-school, please register here. Registration is mandatory and applies to both the pre-school and the summer school on Galois representations and Reciprocity.
Topics:
- Course 1: Algebraic number theory (5 lectures): Ring of integers, unique factorization of ideals, class group, decomposition, inertia group and Frobenius, Chebotarev density theorem, local and global fields, adeles.
Suggested reference: Chapter 1 of “Algebraic Number Theory: Proceedings of an Instructional Conference Organized by the London Mathematical Society”, J.W.S.Cassels (editor) and A.Frohlich (editor). - Course 2: Class field theory (2 lectures): statement of local and global class field theory, maybe examples if there is time.
Suggested reference: “Algebraic Number Theory: Proceedings of an Instructional Conference organized by the London Mathematical Society”, J.W.S.Cassels (editor), A.Frohlich (editor), or “Class Field Theory”, E.Artin and J.Tate. - Course 3: Galois cohomology and Tate duality (3 lectures): cohomology of (pro-)finite groups and basic properties, local and global Tate duality, Poitou-Tate.
Suggested reference: “Cohomology of Number Fields, J.Neukirch, A.Schmidt and K. Wingberg. - Course 4: An introduction to modular forms (4 lectures): modular curves, Hecke operators.
Suggested reference: “A First Course in Modular Forms”, F.Diamond and J.Shurman.