Galois representations

A fifteen-lesson course from profinite Galois groups and elliptic-curve Tate modules to Weil–Deligne representations, modular forms and Serre modularity. All lessons are authored; independent full-course review is pending.

1. Profinite groups and ℓ-adic representations
2. Frobenius elements and determination by traces
3. The ℓ-adic Tate module of an elliptic curve
4. Representations of Weil groups
5. Conductors of Weil-group representations
6. Local L-factors and epsilon factors
7. Weil–Deligne representations and Grothendieck’s monodromy theorem
8. Elliptic curves over local fields and their Weil–Deligne representations
9. Compatible systems and global L-functions
10. Modular curves over Q and the Eichler–Shimura congruence
11. Galois representations of weight-two newforms
12. Deligne's construction in higher weight and the Ramanujan–Petersson bound
13. Weight one: the theorem of Deligne and Serre
14. p-adic Hodge theory and the Fontaine–Mazur conjecture
15. Residual representations and Serre's modularity theorem

Original text CC0 1.0 unless the lesson states other terms.