Study on relative rigid cohomologies and homotopies of arithmetic varieties via logarithmic p-adic analysis

• Project/Area Number: 18740002
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: SHIHO Atsushi The University of Tokyo, 大学院数理科学研究科, 准教授 (30292204)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,740,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: クリスタル / リジッドコホモロジー / 過収束性 / 対数的代数多様体 / p進解析 / 対数的延長 / クリスタルコホモロジー / 重み篩 / 過収束アイソクリスタル / p進非リュービル数 / 重み節 / 重みスペクトル系列 / 収束コホモロジー

Research Abstract

標数p>0の完全体上の代数多様体の射の相対的リジッドコホモロジーの有限性、過収束性を適当な仮定の下で証明した。過収束アイソクリスタルの対数的延長理論を適当な仮定の下で証明した。また、標数p>0の正則優秀スキームの対数的ホッジ・ヴィットコホモロジーに対する純性定理およびガーステン型予想を証明した。更に相対的対数的クリスタルコホモロジーの重み篩の理論を構築した。

Research Products

• [Journal Article] On logarithmic Hodge-Witt cohomology of regular schemes (2007)
  • Author(s): A. Shiho
  • Journal Title: J. Math. Sci. Univ. Tokyo 14 Pages: 567-635
  • NAID: 120001031703
  • Peer Reviewed
• [Journal Article] On Logarithmic Hodge-Witt Cohomology of Regular Schemes (2007)
  • Author(s): Atsushi Shiho
  • Journal Title: Journal of Mathematical Sciences, Univ. of Tokyo 14 Pages: 567-635
  • NAID: 120001031703
  • Peer Reviewed
• [Presentation] On logarithmic extension of overconvergent isocrystals (2008)
  • Author(s): A. Shiho
  • Organizer: p-adic method and its applications in arithmetic geometry at Sendai
  • Place of Presentation: 東北大学
  • Year and Date: 2008-11-07
• [Presentation] On logarithmic extension of overconvergent isocrystals (2008)
  • Author(s): Atsushi Shiho
  • Organizer: p-adic method and its applications in ari thmetic geometry in Sendai
  • Place of Presentation: 東北大学
  • Year and Date: 2008-11-07
• [Presentation] On the overconvergence of relative rigid cohomology (2008)
  • Author(s): A. Shiho
  • Organizer: p-adic differential equations a conference in honor of Gilles Christol
  • Place of Presentation: Bressanone(イタリア)
  • Year and Date: 2008-09-09
• [Presentation] On the overconvergence of relative rigid cohomology (2008)
  • Author(s): Atsushi Shiho
  • Organizer: p-adic differential equatios : a conference in honor of Gilles Christol
  • Place of Presentation: Bressanone(イタリア)
  • Year and Date: 2008-09-09
• [Presentation] On the overconvergence of relative rigid cohomology (2007)
  • Author(s): A. Shiho
  • Organizer: 代数的整数論とその周辺
  • Place of Presentation: 京大数理研
  • Year and Date: 2007-12-11
• [Presentation] Relative log convergent cohomology and relative rigid cohomology (2007)
  • Author(s): A. Shiho
  • Organizer: p-adic aspects in arithmetic geometry
  • Place of Presentation: 玉原国際セミナーハウス
  • Year and Date: 2007-06-05
• [Presentation] Relative log convergent cohomology and relative rigid cohomology II (2006)
  • Author(s): A. Shiho
  • Organizer: p-adic method and its applications in arithmetic geometry
  • Place of Presentation: 広島大学
  • Year and Date: 2006-11-25
• [Presentation] Relative log convergent cohomology and relative rigid cohomology (2006)
  • Author(s): A. Shiho
  • Organizer: $p$-adic Arithmetic Geometry
  • Place of Presentation: 京大数理研
  • Year and Date: 2006-11-22
• [Book] Weight filtrations on log crystalline cohomologies of families of open smooth varieties, Lecture Note in Mathematics 1959 (2008)
  • Author(s): Y. Nakkajima and A. Shiho
  • Total Pages: 266
  • Publisher: Springer Verlag
• [Book] Weight filtrations on log crystalline cohomologies of families of open smooth varieties (2008)
  • Author(s): Yukiyoshi Nakkajima and Atsushi Shiho
  • Total Pages: 266
  • Publisher: Springer Verlag