Research on p-adic Hodge theory

• Project/Area Number: 21840001
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: MORITA Kazuma Hokkaido University, 大学院・理学研究院, 助教 (40548187)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,704,000 (Direct Cost: ¥2,080,000、Indirect Cost: ¥624,000); Fiscal Year 2010: ¥1,287,000 (Direct Cost: ¥990,000、Indirect Cost: ¥297,000); Fiscal Year 2009: ¥1,417,000 (Direct Cost: ¥1,090,000、Indirect Cost: ¥327,000)
• Keywords: p進表現 / p進微分方程式 / p進Hodge理論

Research Abstract

We study the p-adic analogy of the Griffiths transversality of Gauss-Manin connections which plays the essential roles in the deformation theory of classical Hodge structures. Furthermore, we propose that there also exists an analogy theory if we regard an integral arithmetic variety as a family over the spectrum of a ring of integers.

Research Products

• [Journal Article] Hodge-Tate and de Rham representations in the imperfect residue field case. (2010)
  • Author(s): 森田知真
  • Journal Title: Ann.Sci.Ec.Norm.Super.(4) 43 no.2 Pages: 341-356
  • Peer Reviewed
• [Journal Article] Hodge-Tate and de Rham representations in the imperfect residue fieldcase (2010)
  • Author(s): Kazuma Morita
  • Journal Title: Ann. Sci. Ec. Norm. Super. Volume: 43(4) Pages: 341-356
  • Peer Reviewed
• [Presentation] Generalization of the theory of Sen in the semi-stable representation case. (2010)
  • Author(s): 森田知真
  • Organizer: 数論幾何セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-09-22
• [Presentation] Generalization of the theory of Sen (2010)
  • Author(s): Kazuma Morita
  • Organizer: 数論幾何セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-09-22
• [Presentation] Generalization of the theory of Sen in the semi-stable representation case. (2010)
  • Author(s): 森田知真
  • Organizer: Workshop on arithmetic geometry at Tambara
  • Place of Presentation: 東京大学国際玉原セミナーハウス
  • Year and Date: 2010-05-26
• [Presentation] Generalization of the theory of Sen in the semi-stable representation case (2010)
  • Author(s): Kazuma Morita
  • Organizer: Workshop on arithmetic geometry at Tambara, 2010
  • Place of Presentation: 東京大学玉原国際セミナーハウス 招待講演
  • Year and Date: 2010-05-26
• [Presentation] Introduction on Representa-tions p-adique cristallines et de de Rham dans le cas relatif. (2010)
  • Author(s): 森田知真
  • Organizer: Workshop on arithmetic geometry at Tambara
  • Place of Presentation: 東京大学国際玉原セミナーハウス
  • Year and Date: 2010-05-25
• [Presentation] Repr'esentations p-adiques cristallines et de de Rham dans lecas relative (2010)
  • Author(s): Kazuma Morita
  • Organizer: Workshop on arithmetic geometry at Tambara, 2010
  • Place of Presentation: 東京大学玉原国際セミナーハウス 招待講演
  • Year and Date: 2010-05-25
• [Presentation] Relative p-adic Hodge theory (2009)
  • Author(s): 森田知真
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-05-15
• [Presentation] Relative p-adic Hodge theory (2009)
  • Author(s): 森田知真
  • Organizer: 北海道大学談話会
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-05-07
• [Presentation] p-adic Hodge theory (3 talks) (2009)
  • Author(s): 森田知真
  • Organizer: ASARCS eminar
  • Place of Presentation: KAIST(韓国,テジョン)
• [Presentation] p進Hodge理論入門(4 talks) (2009)
  • Author(s): 森田知真
  • Organizer: 数論幾何セミナー
  • Place of Presentation: 北海道大学
• [Remarks] ホームページ等
  • URL: http://kazuma-morita.jimdo.com/