Algebraic cycles and Iwasawa theory
-
- Kobayashi Shinichi
- Principal Investigator
- 九州大学
-
- 千田 雅隆
- Co-Investigator
- 東京電機大学
-
- 大坪 紀之
- Co-Investigator
- 千葉大学
-
- 落合 理
- Co-Investigator
- 大阪大学
About this project
- Japan Grant Number
- JP17H02836
- Funding Program
- Grants-in-Aid for Scientific Research
- Funding organization
- Japan Society for the Promotion of Science
- Project/Area Number
- 17H02836
- Research Category
- Grant-in-Aid for Scientific Research (B)
- Allocation Type
-
- Single-year Grants
- Review Section / Research Field
-
- Science and Engineering > Mathematics and Physics > Mathematics > Algebra
- Research Institution
-
- Kyushu University
- Project Period (FY)
- 2017-04-01 〜 2022-03-31
- Project Status
- Completed
- Budget Amount*help
- 15,470,000 Yen (Direct Cost: 11,900,000 Yen Indirect Cost: 3,570,000 Yen)
Research Abstract
First, we studied generalized Heegner cycles and the anticyclotomic Iwasawa theory of modular forms, and constructed the Perrin-Riou theory interpolating generalized Heegner cycles p-adically even at non-ordinary primes. Especially, we constructed the thery of integral Perrin-Riou twist, which is a generalization and a refinement of the original one. Then, with Kazuto Ota of Osaka University, we proved a half of the inequality of the Iwasawa main conjecture in this setting under relatively mild conditions. Later, in collaboration with Ota and Ashay Burungale of California Institute of Technology (now University of Texas), we studied the anticyclotomic Iwasawa theory of CM elliptic curves at inert primes , and solved the Rubin conjecture, which had been unsolved for more than 30 years.