Research on p-adic Hodge theory with arithmetic D-modules

• Project/Area Number: 21540008
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TSUJI Takeshi 東京大学, 大学院・数理科学研究科, 教授 (40252530)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: p進Hodge理論 / 数論的D加群 / p進perverse層

Research Abstract

Takeshi Tsuji studied p-adic Hodge theory for p-adic perverse sheaves on a poper smooth algebraic variety with good reduction over a p-adic field, and generalized the notion of crystalline sheaves for local systems to perverse sheaves whose singular locus lies on a simple normal crossing divisor. He also studied the weight spectral sequence of p-adic cohomology constructed from nearby cycles D-modules, and proved its functoriality and its compatibility with duality, Frobenius automorphisms, and algebraic correspondences.

Research Products

• [Journal Article] Purity for Hodge-Tate representations (2011)
  • Author(s): T. Tsuji
  • Journal Title: Mathematische Annalen Volume: 350 Issue: 4 Pages: 829-866
  • DOI: 10.1007/s00208-010-0582-7
  • Peer Reviewed
• [Journal Article] p-adic perverse sheaves and filtered arithmetic D-modules with singularities along a normal crossing divisor, Algebraische Zahlentheorie 2011 (2011)
  • Author(s): T. Tsuji
  • Journal Title: Mathematisches Forschungsinstitut Oberwolfach Report Volume: 31 Pages: 1735-1738
• [Journal Article] p-adic perverse sheaves and arithmetic D-modules with singularities along a normal crossing divisor (2011)
  • Author(s): 辻雄
  • Journal Title: Algebraische Zahlentheorie 2011, Mathematisches Forschungsinstitut Oberwolfach Report Volume: 31 Issue: 2 Pages: 1735-1738
  • DOI: 10.4171/owr/2011/31
• [Journal Article] On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves, Annales Scientifiques de l' ENS 43 (2010)
  • Author(s): K. Bannai, S. Kobayashi and T. Tsuji
  • Journal Title: fascicule Volume: 2 Pages: 185-234
  • Peer Reviewed
• [Journal Article] On nearby cycles and D-modules of log schemes incharacteristic p> 0 (2010)
  • Author(s): T. Tsuji
  • Journal Title: Compositio Mathematica Volume: 146 Issue: 6 Pages: 1552-1616
  • DOI: 10.1112/s0010437x10004768
  • Peer Reviewed
• [Journal Article] On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves (2010)
  • Author(s): K.Bannai, S.Kobayashi, T.Tsuji
  • Journal Title: Annales Scientifiques de l'ENS Volume: 43 Pages: 185-234
  • Peer Reviewed
• [Journal Article] On nearby cycles and D-modules of log schemes in characteristic p>0 (2010)
  • Author(s): 辻雄
  • Journal Title: Compositio Mathematica Volume: 146 Pages: 1552-1616
  • Peer Reviewed
• [Presentation] p-adic perverse sheaves and filtered arithmetic D-modules with singularities along a normal crossing divisor (2011)
  • Author(s): 辻雄
  • Organizer: Algebraische Zahlentheorie, Mathematisches Forschungsinstitut Oberwolfach
  • Place of Presentation: Germany
  • Year and Date: 2011-06-22
• [Presentation] p-adic perverse sheaves and arithmetic D-modules with singularitiesalong a normal crossing divisor (2011)
  • Author(s): 辻雄
  • Organizer: Algebraische Zahlentheorie 2011
  • Place of Presentation: Mathematisches Forschung sinstitut Oberwolfach,ドイツ(招待講演)
  • Year and Date: 2011-06-22
• [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve (2010)
  • Author(s): 辻雄
  • Organizer: Arithmetic geometry and p-adic differential equations
  • Place of Presentation: 東北大学
  • Year and Date: 2010-07-02
• [Presentation] Semi-stable reduction and arithmetic D-modules, Current trends in logarithmic geometry (2010)
  • Author(s): 辻雄
  • Organizer: Universite Bordeaux 1
  • Place of Presentation: France
  • Year and Date: 2010-06-24
• [Presentation] Semi-stable reduction and arithmetic D-modules, Current trends in logarithmic geometry (2010)
  • Author(s): 辻雄
  • Organizer: Current trends in logarithmic geometry
  • Place of Presentation: Universite Bordeauxフランス
  • Year and Date: 2010-06-24
• [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve (2010)
  • Author(s): 辻雄
  • Organizer: Conference de Geometrie Arithmetiqueen l'honneur de Jean-Marc Fontaine
  • Place of Presentation: アンリ・ポワンカレ研究所(フランス・パリ)
  • Year and Date: 2010-03-25
• [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve (2010)
  • Author(s): 辻雄
  • Organizer: Conference de Geometrie Arithmetique en l' honneur de Jean-Marc Fontaine, Institute Henri Poincare
  • Place of Presentation: France
• [Presentation] Nearby cycles and D-modules of log schemes in characteristic p> 0 (2009)
  • Author(s): 辻雄
  • Organizer: East Asia Number Theory Conference
  • Place of Presentation: 清華大学,中国
  • Year and Date: 2009-08-20
• [Presentation] Nearby cycles and D-modules of log schemes in characteristic p>0 (2009)
  • Author(s): 辻雄
  • Organizer: East Asia Number Theory Conference
  • Place of Presentation: 清華大学(中国・北京)
  • Year and Date: 2009-08-20
• [Presentation] Arithmetic D-modules and weight spectral sequences, Journees de Geometrie Arithmetique de Rennes (2009)
  • Author(s): 辻雄
  • Organizer: Institut de Recherche Mathematique de Rennes
  • Place of Presentation: France
  • Year and Date: 2009-07-07
• [Presentation] Arithmetic D-modules and weight spectral sequences (2009)
  • Author(s): 辻雄
  • Organizer: Journees de Geometrie Arithmetique de Rennes
  • Place of Presentation: レンヌ数学研究所(フランス・レンヌ)
  • Year and Date: 2009-07-07