- Ribet’s converse to Herbrand theorem
- Deligne-Ribet p-adic L-functions
- Wiles’ proof for Iwasawa main conjecture for GL_1 over totally real fields

Date | Title | Speaker | Reference | Notes |
---|---|---|---|---|

9/19 | Basic definitions and properties for Eisenstein series (1) | Vivian Yu | [Sh] | note |

9/26 | Basic definitions and properties for Eisenstein series (2) | David Marcil | [BL] | note |

10/3 | Ribet's converse to Herbrand theorem | Yu-Sheng Lee | [Wa], [Ri] | note |

10/10 | Eisenstein series on GL_2 | Hung Chiang | [Bu], [JL] | |

10/17 | Hida theory for GL_2 over totally real fields | Haodong Yao | [Wi1] | |

10/24 | Deligne-Ribet p-adic L-functions | David Marcil | [DR] | |

10/31 | Review of Iwasawa theory and main conjecture | Michele Fornea | [Wa] | |

11/7 | Holiday break | - | - | - |

11/14 | Iwasawa main conjecture for totally real fields (1) | TBD | [Wi2] | |

11/21 | Iwasawa main conjecture for totally real fields (2) | TBD | [Wi2] | |

11/28 | TBD | |||

12/5 | TBD | |||

12/12 | TBD |

[BL] Bernstein, Joseph, and Erez Lapid. "On the meromorphic continuation of Eisenstein series." arXiv preprint arXiv:1911.02342 (2019).

[DR] Deligne, Pierre, and Kenneth A. Ribet. "Values of abelian L-functions at negative integers over totally real fields." Inventiones mathematicae 59.3 (1980): 227-286.

[JL] Jacquet, Hervé, and Robert P. Langlands. Automorphic Forms on GL (2): Part 1. Vol. 114. Springer, 2006.

[Ri] Ribet, Kenneth A. "A modular construction of unramified p-extensions of Q(μp)." Invent. math 34.3 (1976): 151-162.

[Sh] Shahidi, Freydoon. Eisenstein series and automorphic L-functions. Vol. 58. American Mathematical Soc., 2010.

[Wa] Washington, Lawrence C. Introduction to cyclotomic fields. Vol. 83. Springer Science & Business Media, 1997.

[Wi1] Wiles, Andrew. "On ordinary λ-adic representations associated to modular forms." Inventiones mathematicae 94.3 (1988): 529-573.

[Wi2] Wiles, Andrew. "The Iwasawa conjecture for totally real fields." Annals of mathematics 131.3 (1990): 493-540.