2009 Fiscal Year Final Research Report
Study of the moduli of Galois representations
| Project/Area Number |
19540036
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
TAGUCHI Yuichiro Kyushu University, 大学院・数理学研究院, 准教授 (90231399)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
SAITO Takeshi 東京大学, 大学院・数理科学研究科, 教授 (70201506)
HIRATA Noriko 日本大学, 理工学部, 教授 (90215195)
MORISHITA Masanori 九州大学, 大学院・数理学研究院, 教授 (40242515)
|
|---|
| Project Period (FY) |
2007 – 2009
|
| Keywords | Galois表現 / moduli, Serreの保型性予想 / 頂切離散附値環 / 分岐 |
|---|
| Research Abstract |
We constructed a foundational theory of moduli of Galois representations and applied it to some problems in number theory. In particular, we defined a category of extensions of truncated discrete valuation ring with restricted ramification and proved that it does not depend on any choices, and that it is equivalent to the category of finite extensions of a complete discrete valuation field with restricted ramification. Also, in relation to Serre's modularity conjecture for real quadratic fields, we obtained interesting results on the non-existence and finiteness of mod 2 Galois representations of some quadratic fields.
|
