Introduction to Drinfeld modules

✍ Scribed by Bjorn Poonen

• Tongue: English
• Leaves: 20
• Category: Library

✦ Table of Contents

1. Applications
2. Analytic theory
   2.1. Inspiration from characteristic 0
   2.2. Characteristic p analogues
3. Algebraic theory
   3.1. Fq-linear polynomials
   3.2. Drinfeld modules
   3.3. Rank
   3.4. Analogies
   3.5. Height
   3.6. Drinfeld modules and lattices
   3.7. Torsion points
   3.8. Tate modules
4. Reduction theory
   4.1. Drinfeld modules over rings
   4.2. Good and stable reduction
5. Example: The Carlitz module
6. Class field theory
   6.1. The class group
   6.2. Rank 1 Drinfeld modules over C
   6.3. The action of ideals on Drinfeld modules
   6.4. Sgn-normalized Drinfeld modules
   6.5. The narrow Hilbert class field
   6.6. The Hilbert class field
   6.7. Ray class fields
   6.8. The maximal abelian extension
   6.9. Example of an explicit Hilbert class field
7. Drinfeld modular varieties
   7.1. Classical modular curves
   7.2. Drinfeld modular curves
   7.3. Drinfeld modular varieties and stacks
   Acknowledgements
   References