Modular Curves and the Eisenstein Ideal

Draft program: see here (to be updated).

Logistics:

There will be a coffee break from 15:30 to 16:00, followed by the Number Theory Seminar from 16:00 to 17:00 (the NT seminar starts on 6th May).

Main references:

[Mar77] Barry Mazur. Modular curves and the Eisenstein ideal. Publ. Math. Inst. Hautes Études Sci. 47.1 (1977): 33-186.
[Sno13] Andrew Snowden’s lecture notes.

The following resources might be helpful as well:

Seminar notes on Mazur’s theorem at Michigan, which contains some more detailed expositions of Mazur’s theorem and related topics
Niven Achenjang’s notes from Snowden’s course
Jan Vonk’s Séminaire Mazur, which contains some references for background material
Study group notes on Mazur’s Torsion Theorem at Paris 13

Time	Content	Speaker	Notes/References
29 Apr	Overview	Netan	notes, § 3.5 [Maz77]
06 May	Admissible group schemes	Shin Thant	notes, hand-out
13 May	Abelian varieties, Jacobians, and their Néron models	Naina	notes, hand-out
20 May	Modular curves and the proof of Theorem A	Yiannis	notes
27 May	Toric reduction of Jacobian of modular curves	Jed
03 June	The proof of Theorem B	Yicheng
10 June	Hecke algebras and the Eichler--Shimura relation	Julian
17 June	The Eisenstein ideal	Andrew
24 June	Finishing up	David and Simon