Teacher: Xavier Caruso
Program:
- 1. Introduction: Carlitz module, Carlitz zeta function
- 2. Definition of Drinfeld modules
- 2.1. Analytic definition
- 2.2. Algebraic definition
- 2.3. Uniformization theorem
- 2.4. Structure of rank-1
- 3. Drinfeld modules
- Drinfeld modules over finite fields
- 3.1. The Frobenius endomorphism
- 3.2. Structure of the endomorphism ring
- 4. Drinfeld modules over function fields
- 4.1. Reduction modulo 𝑝
- 4.2. 𝐿-functions and Taelman’s class formula