This autumn semester 2021-2022 we will study Mazur's article Modular Curves and the Eisenstein ideal (which can be found here). The seminar will take place every Friday morning 8:30-10:00, at Salle PLT 2504 located in Pavillon Adrien-Pouliot.
2021-09-10 Organisational meeting (Katharina and Jiacheng)
2021-09-17 Generalities on the modular curve of level N (II 1-3) (Luochen)
2021-09-24 Parabolic and non-parabolic modular forms (II 4-5) (Anthony)
2021-10-01 Hecke operators and the Hecke algebra (II 6-7) (Mihir)
2021-10-08 Rank 1 and multiplicity one (II 8-9) (Anthony)
2021-10-15 The cuspidal and Shimura subgroups (II 11) (Cedric)
2021-10-22 Introduction to admissible groups (reference: Milne’s Algebraic groups) (Katharina)
2021-11-05 The Galois action on the torsion points of the Jacobian (II 14) (Cedric)
2021-11-12 Statement and proof of Theorem 8 (III 5) (Katharina)
2021-11-19 The Gorenstein condition and Eisenstein primes (II 15-17) (Mihir)
2021-11-26 Statement and proof of Theorem 1 (II 10 and III 1) (Antonio)
2021-12-03 CM points, the Mordell—Weil group of the Jacobian, and Theorem 3, 4 (III 2-3) Jiacheng)
2021-12-10 Statement and proof of Theorem 6 (III 4) (Jiacheng)