Iwasawa theory studies arithmetic objects in certain p-adic towers of number fields. In this seminar we will focus on the classical case of Z_p-extensions. We will discuss and prove the structure theory of finitely generated modules over the Iwasawa algebra. This will then allow us to derive Iwasawa's theorem on the behaviour of the p-part of the class number in a Z_p-extension of a number field.
Then we will move on to elliptic curves, treating the contents of Greenberg's Introduction to Iwasawa Theory for Elliptic Curves. The principal result that we will obtain will be a theorem of Mazur's stating that the rank of an elliptic curve in a Z_p-extension of a number field F is bounded if the Mordell-Weil group and the p-part of the Tate-Shafarevich-group at F are finite.
If time allows, we will make first steps on towards p-adic L-functions and Iwasawa's main conjecture.
The final version of the programme can be downloaded here.
| Date | Title | Speaker |
| 09/04/2008 | Introduction | Gabor Wiese |
| 16/04/2008 30/04/2008 | Z_p-extensions | Adam Mohamed |
| 23/04/2008 | No seminar due to the inauguration ceremony. | --- |
| 30/04/2008 07/05/2008 14/05/2008 | The completed group algebra and class groups in Z_p-extensions | Eduardo Ocampo |
| 14/05/2008 21/05/2008 | The Iwasawa algebra (notes) | Marcel Mohyla |
| 28/05/2008 | Modules of the Iwasawa algebra | Ralf Butenuth |
| 04/06/2008 | Iwasawa's theorem (notes) | Marios Magioladitis |
| 11/06/2008 18/06/2008 | Some Galois cohomology | Eduardo Ocampo |
| 25/06/2008 | Elliptic curves and Galois cohomology (I) | Gabor Wiese |
| 02/07/2008 | Elliptic curves and Galois cohomology (II) | Björn Buth |
| 09/07/2008 | Mazur's control theorem | Oscar Ledesma |
| 16/07/2008 | Corollaries of Mazur's control theorem (slides) | Lassina Dembélé |
Last modification: 12 August 2008.