L-functions and motivic cohomology of arithmetic varieties and applications to cyclotomic fields
| Project/Area Number |
25400007
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Chiba University |
|---|
Principal Investigator |
Otsubo Noriyuki 千葉大学, 大学院理学研究院, 准教授 (60332566)
|
|---|
| Project Period (FY) |
2013-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | モチーフ / L関数 / モチーフ的コホモロジー / 超幾何関数 / 円分体 / レギュレーター / 周期 / フェルマー多様体 / 周期予想 / ヤコビ和 / 虚数乗法 / Ｌ関数 / イデアル類群 |
|---|
| Outline of Final Research Achievements |
We studied relations between L-functions of arithmetic varieties and their applications to cyclotomic fields. In particular, we obtained new relations between special values of Hecke L-functions of cyclotomic fields and motivic cohomology of Fermat motives, in terms of generalized hypergeometric functions. On the other hand, we defined a new class of families of varieties called hypergeometric fibrations, and for such families, proved the Gross-Deligne conjecture on periods and expressed the regulators in terms of generalized hypergeometric functions. Moreover, we determined the structure of the profinite homology of the tower of Fermat curves, and by using this, gave a simple construction of Ihara-Anderson's universal measure of Jacobi sums.
|
Report
(6 results)
Research Products
(22 results)
