Hodge theory, mixed motives and regulator

• Project/Area Number: 18740012
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hokkaido University (2008); Kyushu University (2006-2007)
• Principal Investigator: ASAKURA Masanori Hokkaido University, 大学院理学研究院, 準教授 (60322286)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,710,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: ホッジ理論 / 混合モチーフ / レギュレーター / 代数K理論 / 代数 K 理論

Research Abstract

P進局所体上の楕円曲面のK_2についてのテイト予想について実質的な成果をあげることができた。
また、その結果、K_1のp進レギュレーターについて、非消滅のための数値的な条件を得ることができた。
これらの結果を応用することで、0サイクルのなすチャウ群のねじれ部分群が有限になるような曲面の例を構成することに成功した。

Research Products

• [Journal Article] Maximal components of Noether-Lefschetz locus for Beilinson-Hodge cycles (2009)
  • Author(s): M. Asakura and S. Saito
  • Journal Title: Math. Ann 341
  • Peer Reviewed
• [Journal Article] Beilinson's Tate conjecture for K2 of elliptic surface : a survey and examples (2009)
  • Author(s): M. Asakura and K. Sato
  • Journal Title: To appear in the proceedings of TIFR (to appear)
  • Peer Reviewed
• [Journal Article] Correction to ``Surjectivity of p-adic regulators on K_2 of Tate curves (2008)
  • Author(s): M. Asakura
  • Journal Title: Invent. Math 172
  • Peer Reviewed
• [Journal Article] Maximal components of Noether-Lefschetz locus for Beilinson-Hodge cycles (2008)
  • Author(s): M.Asakura and S. Saito
  • Journal Title: Math. Ann 341 Pages: 169-199
  • Peer Reviewed
• [Journal Article] Maximal components of Noether-Lefschetz locus for Beilinson-Hodge cycles (2008)
  • Author(s): M., Asakura・S., Saito
  • Journal Title: Math. Ann. (in press)
  • Peer Reviewed
• [Journal Article] Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles (2007)
  • Author(s): M. Asakura and S. Saito
  • Journal Title: Algebra Number Theory 1 2
  • Peer Reviewed
• [Journal Article] Beilinson's Hodge Conjecture with Coefficients (2007)
  • Author(s): M. Asakura and S. Saito
  • Journal Title: in Algebraic cycles and Motives Volume 2 (for J. Murre's 75th Birthday)London Math. Soc. Lecture Note Ser Cambridge Univ. Press 344 Pages: 3-37
  • Peer Reviewed
• [Journal Article] Beilinaon's Hodge Conjecture with Coefficients (2007)
  • Author(s): M., Asakura・S., Saito
  • Journal Title: Algebraic cycles and Motives(for J. Murre's 75-th Birthday) Vol.2 Pages: 3-37
  • Peer Reviewed
• [Journal Article] Surfaces over a P-adic field with infinite torsion in the Chow group of 0-cycles. (2007)
  • Author(s): M., Asakura・S., Saito
  • Journal Title: Algebra & Number Theory 1 Pages: 163-181
  • Peer Reviewed
• [Journal Article] Surjectivity of p-adic regulators on K_2 of Tate curves (2006)
  • Author(s): M. Asakura
  • Journal Title: Invent. Math 165 Pages: 267-324
  • Peer Reviewed
• [Journal Article] Noether-Lefschetz locus for Beilinson-Hodge cycles I (2006)
  • Author(s): M. Asakura and S. Saito
  • Journal Title: Math. Z 252 Pages: 251-273
  • Peer Reviewed
• [Journal Article] Generalized Jacobian rings for open complete intersections (2006)
  • Author(s): M. Asakura and S. Saito
  • Journal Title: Math. Nachr 279 Pages: 5-37
  • Peer Reviewed
• [Journal Article] Surjectivity of $p$-adic regulators on K_2 of Tate curves. (2006)
  • Author(s): M.AsaKura
  • Journal Title: Invent. Math. 165 Pages: 267-324
• [Journal Article] Noether-Lefschetz locus for Beilinson-Hodage cycles. I. (2006)
  • Author(s): M.Asakura, S.Saito
  • Journal Title: Math.Zeit. 252 Pages: 251-273
• [Journal Article] Generalized Jacobian rings for open complete intersections. (2006)
  • Author(s): M.Asakura, S.Saito
  • Journal Title: Math. Nachr. 279 Pages: 5-37
• [Journal Article] Beilinson's Tate conjecture for K_2 : survey and examples
  • Author(s): M.Asakura and K.Sato
  • Journal Title: Proceedings of TIFR
• [Journal Article] Local units are generated by certain cyclotomic units
  • Author(s): M.Asakura
  • Journal Title: 京都大学数理解析研究所講究録別冊
  • Peer Reviewed
• [Presentation] An elliptic K3 over Qp with finitely many torsion O-cycles (2009)
  • Author(s): M. Asakura
  • Organizer: Workshop : Industrious Number theory
  • Place of Presentation: KIAS(韓国高等研究所)
  • Year and Date: 2009-03-11
• [Presentation] An elliptic K3 surface over Q_p with finitely many torsion 0-cycles (2009)
  • Author(s): M.Asakura
  • Organizer: Workshop: Industrious Number theory KIAS
  • Place of Presentation: 韓国高等研究所
• [Presentation] Non-vanishing of p-adic regulator on K_1 of elliptic surface (2009)
  • Author(s): M.Asakura
  • Organizer: Algebraic geometry seminar KAIST
  • Place of Presentation: 韓国工科大学
• [Presentation] Nonvanishing of p-adic regulator on K_1 of Elliptic surface (2008)
  • Author(s): M.Asakura
  • Organizer: Arithmetic geometry seminar
  • Place of Presentation: Regensburg university
  • Year and Date: 2008-10-31
• [Presentation] Indecomposable K_1 of elliptic surface and non-vanishing p-adic regulator (2008)
  • Author(s): M, Asakura
  • Organizer: International Colloquium Cycles, Motives and Shimura varieties
  • Place of Presentation: タタ研究所(インド)
  • Year and Date: 2008-01-04
• [Presentation] Beilinson's Tate conjecture on K_2 of elliptic surface Workshop: Algebraic cycles (2008)
  • Author(s): M.Asakura
  • Organizer: motives and Shimura variety
  • Place of Presentation: TIFR タタ研究所
• [Presentation] Chow group of 0-cycles on surface over a p-adic field with infinite torsion subgroup (2007)
  • Author(s): M.Asakura
  • Organizer: 国際シンポジウム Motives related topics applications 2007
  • Place of Presentation: 広島大学