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

2016 Fiscal Year Final Research Report

• 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)
• 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
• Keywords: 境界値問題 / Ｄ加群 / 層

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.

Free Research Field

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