| April 2 (Thu), 2009, Seminar Room 305 | |||
|---|---|---|---|
| 9:30-11:00 | 11:15-12:15 | 13:30-15:00 | 15:30-17:00 |
| Kato | Aoki | Buyukboduk | Ochiai |
| 9:30-11:00 | Kazuya Kato (Kyoto University) |
| Introduction to non-commutative Iwasawa theory | |
Abstract:This is an introduction to non-commutative Iwasawa theory of motives,
mainly basing on the paper "T. Fukaya and K. Kato, A formulation of
conjectures on p-adic L-functions in non-commutative Iwasawa theory"
Amer. Math. Soc. Transl. (2006). I explain the non-commutative Iwasawa
main conjecture for general motives.Introduction to non-commutative Iwasawa theory
| |
| [Handwritten Notes (PDF)] | |
| 11:15-12:15 | Miho Aoki (Okayama University of Science) |
| K-groups of rings of algebraic integers and Iwasawa theory | |
Abstract:The K-groups and etale cohomology groups of the rings of algebraic
integers are closely connected with some classical conjectures on
the number theory. In this talk, we will discuss the relations from
the viewpoint of Iwasawa theory. | |
| [Slides of the talk (PDF)] [Webpage of the speaker (in Japanese)] | |
| Lunch | |
| 13:30-15:00 | Kazim Buyukboduk (Max-Planck-Institut fur Mathematik / Koc University) |
| Euler systems of rank r and their Kolyvagin systems | |
Abstract:
For a p-adic Galois representation T, I will devise an Euler system/Kolyvagin
system machinery which as an input takes an Euler system
of rank r (in the sense of Perrin-Riou), and gives a bound on
the Bloch-Kato Selmer group in terms of an r x r determinant. I will
give two fundamental applications of this refinement: The first with
the (conjectural) Rubin-Stark elements; and the second with
Perrin-Riou's (conjectural) p-adic L-functions. | |
| [Handwritten Notes (PDF)] [Webpage of the speaker] | |
| Coffee/Tea | |
| 15:30-17:00 | Tadashi Ochiai (Osaka University) |
| On conjectural framework for generalized Iwasawa theory | |
Abstract:
In this talk, we present the idea on the generalization of Iwasawa
theory for Galois deformation spaces. We will explain elementary
aspects of the theory with several basic examples rather than talking
about our own results. For example, we try to discuss the most
general conjectural framework for the existence of p-adic L-function
and compare it with known examples. | |
| [Handwritten Notes (PDF)] [Webpage of the speaker] | |
This workshop is supported by Japan Society for the Promotion of Science Grant-in-Aid for Young Scientists (S) ``Comprehensive studies on Shimura varieties, arithmetic geometry, Galoisrepresentations, and automorphic representations'' (20674001).