Geometry of defomation spaces of Galois representations, p-adic Hodge theory and Langnands duality

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540018
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: YASUDA Seidai 大阪大学, 理学(系)研究科(研究院), 准教授 (90346065)
• Co-Investigator(Kenkyū-buntansha): KONDO Satoshi 東京大学, カブリ数物連携宇宙研究機構, 客員准科学研究員 (30372577) ; TAGUCHI Yuichiro 九州大学, 数理学研究院, 准教授 (90231399) ; HIRANOUCHI Toshiro 広島大学, 理学研究科, 助教 (30532551)
• Co-Investigator(Renkei-kenkyūsha): TSUJI Takeshi 東京大学, 数理科学研究科, 教授 (40252530)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ガロア表現 / p 進 Hodge 理論 / 多重ゼータ値

Outline of Final Research Achievements

The main researcher of this project and Go Yamashita computed the reductions modulo p of two dimensional crystalline representations except for a small number of exceptions when the difference of Hodge-Tate weights are less than or equal to (p-1)/2, and investgate a proof of comparison theorem of cohomologies of open varieties over p-adic fields and prepare fundamental tools to complete the proof. He, Kazuma Akagi, and Minoru Hirose proved that the p-adic multiple zeta values of weight k belongs to the k-th PD-ideal of pZ_p, and using this, gave a upper bound of the dimension of the Q-vector space of finite multiple zeta values inroduced by Kaneko and Zagier.

Free Research Field

整数論