2020 Spring: Herbrand-Ribet theorem and the Iwasawa main conjecture

References for the class:

• K. Ribet, A modular construction of unramified p-extension of Q(mu_p), [link]
• A. Wiles, Modular curves and the class group of Q(zeta_p), [link]
• Washington, Introduction to cyclotomic fields.
• Lang, Cyclotomic fields I and II.
• J. Coates and R.Sujatha, Cyclotomic fields and zeta values.
• Ribet's slide : [pdf]
• Khare's survey : [pdf]
• Wang-Erickson's survey : [link] (and his note on cyclotomic fields [link]
• M. Raynaud, Modular curves and the Hecke operators (translation) [pdf]

References for Class field Theory:

• Cassels and Frohlich, Algebraic Number theory
• Milne, Class field theory, [link]
• Neukirch, Class field theory, [link]
• Guillot, A Gentle Course in Local Class Field Theory (elementary)
• Serre, Local fields (advanced)
• Student's minor thesis on Tate's thesis, [link]
• Buzzard, Tate's thesis, [link] (recommended)
• Ramakrishnan and Valenza, Fourier analysis on Number fields (thorough exposition on Tate's thesis)

Reference for Modular forms:

• Ullmo, Modular curves and Modular forms, [link]
• Ribet and Stein, Lectures on modular forms, [link]
• Helm, Modular forms, [link]
• Milne, Modular functions and modular forms, [link]
• Diamond and Shurman, A first course in modular forms.
• Schraen, Modular curves, [link]

Reference for compact Riemann surfaces:

• Kirwan, Complex algebraic curves.
• Griffiths, Introduction to algebraic curves.
• Miranda, Algebraic curves and Riemann surfaces

Lecture videos : [link]

Lecture notes

1. Lecture 1 [pdf]
2. Lecture 2 [pdf]
3. Lecture 3 [pdf]
4. Lecture 4 [pdf]
5. Lecture 5 [pdf]
6. Lecture 6 [pdf]
7. Lecture 7 [pdf]
8. Lecture 8 [pdf]
9. Lecture 9 [pdf]
10. Lecture 10 [pdf]
11. Lecture 11 [pdf]
12. no notes
13. Lecture 13 [pdf]
14. Lecture 14 [pdf]
15. Lecture 15 [pdf]
16. Lecture 16 [pdf]
17. no notes
18. Lecture 18 [pdf]
19. Lecture 19 [pdf]
20. Lecture 20 [pdf]
21. Lecture 21 [pdf]
22. Lecture 22 [pdf]