In the fall 2017 semester Dave Hansen and I organized a seminar on Hida Theory.
Time and place: Thursdays 1:00-2:15 in Mathematics 622.
Here are notes, taken by Pak-Hin Lee.
References:
Lecture 1 was based off Chapter 2 of Christopher Skinner's CMI notes, "Galois Representations, Iwasawa Theory, and Special Values of L-functions."
Lecture 2 contains material that can be found, for instance, in Lang's "Cyclotomic Fields I and II." See Chapter 5.
Lectures 4-7 by Pak-Hin Lee used Hida's blue book, "Elementary Theory of L-functions and Eisenstein Series."
He also used the notes of Banerjee-Ghate-Kumar, "\Lambda-adic Forms and the Iwasawa Main Conjecture."
Lecture 8 (the first one on the proof of the main conjecture) used Fitting ideals. A nice reference containing all of the facts I used is Nuccio's notes "Fitting Ideals."
Tentative Schedule:
| Date | Title | Speaker |
|---|---|---|
| September 7 | Ribet's Converse to Herbrand's Theorem | Sam Mundy |
| September 14 | Basic Iwasawa Theory | Sam Mundy |
| September 21 | p-Adic Properties of L-Functions | Sam Mundy |
| September 28 | \Lambda-adic Modular Forms | Pak-Hin Lee |
| October 5 | Ordinary \Lambda-adic Forms | Pak-Hin Lee |
| October 12 | Hida Theory and \Lambda-adic Galois Representations | Pak-Hin Lee |
| October 19 | \Lambda-adic Representations via Pseudo-representations | Pak-Hin Lee |
| October 26 | Proof of the Main Conjecture for Q, I | Sam Mundy |
| November 2 | Proof of the Main Conjecture for Q, II | Sam Mundy |
| November 9 | No Talk: IAS Workshop | |
| November 16 | Rescheduled (see below) | |
| November 20 | Higher Hida Theory I (5:00 in room 528) | Dave Hansen |
| November 23 | No Talk: Thanksgiving | |
| November 30 | Higher Hida Theory II | Dave Hansen |
| December 7 | Higher Hida Theory III | Dave Hansen |
| December 14 | No Talk: EPFL Conference |