Strategic Research to solve certain conjectures in Arithmetic Geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 21674001
• Research Category: Grant-in-Aid for Young Scientists (S)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Keio University
• Principal Investigator: BANNAI Kenichi 慶應義塾大学, 理工学部, 准教授 (90343201)
• Research Collaborator: YAMAMOTO Shuji 慶應義塾大学, 理工学部, 特任助教 ; TAKAI Yuki 慶應義塾大学, 理工学部, 特任助教 (90599698) ; MIURA Takashi 慶應義塾大学, 理工学部 (60631934) ; NAKAMURA Kentaro 慶應義塾大学, 理工学部, 特任助教 (90595993) ; ARAI Keisuke 慶應義塾大学, 理工学部, 特任助教 (80422393) ; HAGIHARA Kei 慶應義塾大学, 理工学部, 特任助教 (30512173) ; KASHIO Tomokazu 慶應義塾大学, 理工学部, 特任助教 (10403106) ; OTSUKI Rei 慶應義塾大学, 理工学部, 特任助教 ; HASEGAWA Yasuko 慶應義塾大学, 理工学部, 特任助教 ; TSUSHIMA Takahiro 慶應義塾大学, 理工学部, 研究員 (70583912) ; HIROTSUNE Tomoki 慶應義塾大学, 理工学部 ; ONO Masataka , 慶應義塾大学, 理工学部 ; KINGS Guido Regensburg大学, Lehrstuhl für Reine Mathematik, 教授
• Project Period (FY): 2009-05-11 – 2014-03-31
• Keywords: 楕円曲線 / 虚数乗法 / Hecke指標 / ポリログ / p進L関数 / p進Beilinson予想

Outline of Final Research Achievements

Working on previous research concerning arithmetic geometric object called the “polylogarithm,” we formed a group of young researchers and attacked certain conjectures in arithmetic geometry. We succeeded in solving the p-adic Beilinson conjecture for certain Hecke characters of an imaginary quadratic field. This result is first such result in the non-cyclotomic case. We then discovered a potential candidate for the expression of the polylogarithm in the Hilbert modular case. We expect this candidate will play an important role in solving conjectures in arithmetic geometry.

Free Research Field

代数学