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).
Program (PDF version, in Japanese)
| 10:00-12:00 | 13:30-14:30 | 15:00-16:30 | ||
|---|---|---|---|---|
| April 3 (Sat) | Hsieh (1) | Takemori | Lemma | |
| 10:00-12:00 | 13:30-14:30 | 15:00-17:00 | 19:00- | |
| April 4 (Sun) | Hsieh (2) | Ohshita | Hsieh (3) | (Banquet) |
| 10:00-12:00 | 13:30- | |||
| April 5 (Mon) | Hsieh (4) | (Free/Discussion) | ||
| April 3 (Sat), 2010 | |
| 10:00-12:00 | Ming-Lun Hsieh (National Taiwan University) |
| Lecture (1): Eisenstein congruence on unitary groups | |
Abstract: We will explain the general strategy of Eisenstein congruence which is used to construct sufficiently many elements in Selmer groups in terms of L-values. After a quick review of Wiles' proof of the main conjecture for GL(1) over totally real fields, we willl talk about the main conjecture for CM elliptic curves over general totally real fields for which one needs to study Eisenstein congruence on U(2,1) over totally real fields. | |
| [Handwritten Notes (PDF)] | |
| 13:30-14:30 | Shou Takemori (Kyoto University) |
| A p-adic limit of Siegel Eisenstein series of degree 2 | |
Abstract: We will introduce that a p-adic limit of Siegel Eisenstein series is also Siegel Eisenstein series of degree 2 and there exists a p-adic analytic family of Siegel Eisenstein series of degree 2. | |
| [Handwritten Notes (PDF)] | |
| 15:00-16:30 | Francesco Lemma (Osaka University) |
| A norm compatible system of Galois cohomology classes for GSp(4) | |
Abstract: In the classical case of the Riemann zeta function, the norm compatible system of cyclotomic units gives rise (via the Coleman map) to the Kubota-Leopoldt p-adic zeta function. In general, given a motive M, a conjecture of Perrin-Riou associates a p-adic L-function for M to any norm compatible system of first Galois cohomology classes in the Galois cohomology of the p-adic realization of M. We will discuss the construction of such a norm compatible system related to the rank four motives of GSp(4). | |
| [Handwritten Notes (PDF)] | |
| April 4 (Sun), 2010 | |
| 10:00-12:00 | Ming-Lun Hsieh (National Taiwan University) |
| Lecture (2): Hida theory for unitary groups (I) | |
Abstract: We begin with an introduction to the theory of p-adic modular forms and the definition of Hida's Up-operators for U(2,1)-case. Then we will give a complete description of Hida theory for unitary groups. | |
| [Handwritten Notes (PDF)] | |
| 13:30-14:30 | Tatsuya Ohshita (Kyoto University) |
| The Euler system of cyclotomic units and higher Fitting ideals | |
Abstract: Kurihara established a refinement of the minus-part of the Iwasawa main conjecture of ideal class groups. In this talk, we will explain a result on the higher Fitting ideals of the plus-part. Using the Euler system of cyclotomic units, we will construct ideals of the Iwasawa algebra which give upper bounds of the higher Fitting ideals. This result can be regarded as a refinement of the plus-part of the Iwasawa main conjecture. | |
| [Handwritten Notes (PDF)] | |
| 15:00-17:00 | Ming-Lun Hsieh (National Taiwan University) |
| Lecture (3): Hida theory for unitary groups (II) | |
Abstract: We sketch proofs of the main theorems for ordinary modular forms: (1) The control theorem, (2) The fundamental exact sequence | |
| [Handwritten Notes (PDF)] | |
| 19:00- | (Banquet) |
| April 5 (Mon), 2010 | |
| 10:00-12:00 | Ming-Lun Hsieh (National Taiwan University) |
| Lecture (4): Main conjecture for CM elliptic curves over totally real fields | |
Abstract: We will review the theory of pseudo-representations and explain how to deduce one-side divisibility in the main conjecture for CM elliptic curves over totally real fields from the existence of certain good Hida family of Eisenstein series on U(2,1). | |
| [Handwritten Notes (PDF)] | |
| 13:30- | (Free/Discussion) |