Application of p-adic differential equations to number theory

• Project/Area Number: 19540010
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: MATSUDA Shigeki Chiba University, 大学院・理学研究科, 准教授 (90272301)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 数論 / 数論幾何 / 分岐理論 / p進微分方程式 / p進解析

Research Abstract

Let k be a filed of Laurent series with several variables over an algebraically closed field of positive characteristic and let E be a complete discrete valuation ring of equal characteristic with residue field k. We defined a filtration for a differential module over the Robba ring with residue filed E with respect to the irregularity, which generalized classical filtration defined by Christol and Mebkhout. Then we showed that the filtration coincides with the filtration that comes from the Abbes-Saito filtration on the solution space regarded as Galois module when the differential module can be trivialized by the finite separable extension of the residue field E.

Research Products

• [Presentation] Abbes-Saito filtration and Chiristol Mebkhout filtration (2010)
  • Author(s): 松田茂樹
  • Organizer: Arithmetic geometry and p-adic differential equations
  • Place of Presentation: 東北大学
  • Year and Date: 2010-07-01
• [Presentation] Arithmetic D -module corresponding to rank one representations (2008)
  • Author(s): 松田茂樹
  • 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] Arithmetic D-module corresponding to rank one representations (2008)
  • Author(s): 松田茂樹
  • 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