Study of deformations of Galois representations and special values of p-adic L-functions

2017 Fiscal Year Final Research Report

• 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: Chida Masataka 東北大学, 理学研究科, 助教 (00451518)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: p進L関数 / 岩澤理論 / 一般化Heegnerサイクル / Chow-Heegnerサイクル

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.

Free Research Field

岩澤理論