Study of deformations of Galois representations and special values of p-adic L-functions
Project/Area Number |
15K17509
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Tohoku University |
Principal Investigator |
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | p進L関数 / 岩澤理論 / 一般化Heegnerサイクル / Chow-Heegnerサイクル / p進Gross-Zagier公式 / p進Abel-Jacobi写像 / 反円分的p進L関数 / 一般Heegnerサイクル / Hilbert保型形式 / CM楕円曲線 / 保型形式 / 代数的サイクル / 肥田理論 |
Outline of Final Research Achievements |
In this research, I studied a relation between algebraic cycles and special values of (p-adic) L-functions and I showed an explicit formula between Chow-Heegner cycles and special values of L-functions associated to Hecke characters. I also constructed an algebraic cycle on the product of a Kuga-Sato variety over a Shimura curve associated to an unitary group over a totally real filed and a CM Abelian variety and gave an explicit description of the image of the algebraic cycle under the p-adic Abel-Jacobi map using Coleman integration.
|
Report
(4 results)
Research Products
(21 results)