Mixed motives, algebraic K-theory and regulator

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740001
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: ASAKURA Masanori 北海道大学, 大学院・理学研究院, 准教授 (60322286)
• Project Period (FY): 2009 – 2011
• Keywords: 混合モチーフ / ホッジ理論 / 代数K理論 / レギュレーター

Research Abstract

I studied regulator which is a main topic in this research project. In particular, I had a stimulating research on syntomic regulator on K-groups of elliptic surfaces, and Got results, for example, construction of new elements in the Selmer group of Bloch-Kato. I also got a result on torsion subgroup of Chow group of 0-cycles.

Research Products

• [Journal Article] Beilinson's Tate conjecture for K_2 of elliptic surface : survey and examples (2010)
  • Author(s): 朝倉政典、佐藤周友
  • Journal Title: Tata Institute of Fundamental Research Pages: 35-58
• [Journal Article] Local units are generated by certain cyclotomic units (2009)
  • Author(s): 朝倉政典
  • Journal Title: 京都大学数理解析研究所講究録別B12 Pages: 183-191
• [Journal Article] Quintic surface over p-adic local fields with infinite p-primary torsion in the Chow group of 0-cycles
  • Author(s): 朝倉政典
  • Journal Title: Contemporary Mathematics Volume: (出版予定、印刷中)
• [Journal Article] Syntomic cohomology and Beilinson's Tate conjecture for K_2.
  • Author(s): 朝倉政典, 佐藤周友
  • Journal Title: Journal of Algebraic Geometry Volume: (出版予定、印刷中)
• [Presentation] Explicit computation of syntomic regulator on K_1 of elliptic surface over a p-adic field (2012)
  • Author(s): 朝倉政典
  • Organizer: Workshop on p-adic arithmetic geometry and motives
  • Place of Presentation: 東北大学
  • Year and Date: 20120100
• [Presentation] Note on syntomic regulator and slope (2011)
  • Author(s): 朝倉政典
  • Organizer: Algebraic K-theory and Its Applications
  • Place of Presentation: 南京大学、中国
  • Year and Date: 20110300
• [Presentation] Note on syntomic regulator and slope (2011)
  • Author(s): 朝倉政典
  • Organizer: Arithmetic and Algebraic
  • Place of Presentation: 東京大学
  • Year and Date: 20110100
• [Presentation] Quintic surface over p-adic local fields with infinite p-primary torsion in the Chow group of 0-cycles (2010)
  • Author(s): 朝倉政典
  • Organizer: Regulator III
  • Place of Presentation: バルセロナ大学、スペイン
  • Year and Date: 20100700
• [Presentation] K_2のTate予想とp進レギュレーター (2009)
  • Author(s): 朝倉政典
  • Organizer: 日本数学会秋季総合会
  • Place of Presentation: 大阪大学
  • Year and Date: 20090900