Research on algebraic cycles on arithmetic schemes

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20740008
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Chuo University (2010); Nagoya University (2008-2009)
• Principal Investigator: SATO Kanetomo Nagoya University, 大学院・多元数理科学研究科, 准教授 (50324398)
• Project Period (FY): 2008 – 2010
• Keywords: 数論幾何学

Research Abstract

算術的スキーム、特にp進整数環上の正則半安定族上の1サイクルのChow群の有限性と数論的な性質をコホモロジー的な手法で研究する。

Research Products

• [Journal Article] Kanetomo A finiteness theorem for zero-cycles over p-adic fields. (2010)
  • Author(s): SAITO Shuji, SATO
  • Journal Title: Ann.of Math. 172 Pages: 1593-1639
  • Peer Reviewed
• [Journal Article] Kanetomo A p-adic regulator map and finiteness results for arithmetic schemes. (2010)
  • Author(s): SAITO Shuji, SATO
  • Journal Title: Documenta Math.\ Extra Volume : Andrei A.Suslin's Sixtieth Birthday Pages: 525-594
  • Peer Reviewed
• [Journal Article] Kanetomo l-adic class field theory for regular local rings. (2009)
  • Author(s): SATO
  • Journal Title: Math.Ann. 344 Pages: 341-352
  • Peer Reviewed
• [Presentation] Kanetomo On 1-cycle class maps over p-adic integer rings. (2010)
  • Author(s): SATO
  • Organizer: International workshop on motives in Tokyo, Part 6
  • Place of Presentation: 東京大学
  • Year and Date: 2010-12-13
• [Presentation] On the Chow groups of 0-cycles of varieties over p-adic fields. (2010)
  • Author(s): 佐藤周友
  • Organizer: 代数幾何学城崎シンポジウム
  • Place of Presentation: 城崎大会議館
  • Year and Date: 2010-10-26
• [Presentation] p進数体上の多様体の0 サイクルの有限性について (2010)
  • Author(s): 佐藤周友
  • Organizer: 談話会
  • Place of Presentation: 広島大学
  • Year and Date: 2010-05-27
• [Presentation] Kanetomo Higher cycle class maps for p-adic etale Tate twists. (2009)
  • Author(s): SATO
  • Organizer: 玉原数論幾何研究集会
  • Place of Presentation: 東大玉原国際セミナーハウス
  • Year and Date: 2009-05-26
• [Presentation] 算術的スキームのp進的コホモロジーとサイクル写像. (2009)
  • Author(s): 佐藤周友
  • Organizer: 日本数学会代数学分科会特別講演
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-27