Algebraic analysis of boundary value problems for sheaves and D-modules

• Project/Area Number: 25610019
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: Uchida Motoo 大阪大学, 理学研究科, 准教授 (10221805)
• Co-Investigator(Kenkyū-buntansha): 本多 尚文 北海道大学, 理学(系)研究科(研究院), 教授 (00238817)
• Research Collaborator: Schapira Pierre パリ第6大学, 理学部, 名誉教授
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 境界値問題 / Ｄ加群 / 層 / 超局所解析 / D加群

Outline of Final Research Achievements

The boundary value problems for sheaves and D-modules is formulated and the fundamental theorem is proved. We also considered the initial value problem for systems of micro differential equations and proved the fundamental Cauchy-Kowalevskaja-Kashiwara theorem (an extended version of Cauchy-Kowalevskaja theorem taking cohomology of any degree into consideration) in terms of microlocalization of sheaves.