global problems on non-commutative algebraic geometry

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540044
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kochi University
• Principal Investigator: Tsuchimoto Yoshifumi 高知大学, 教育研究部自然科学系理学部門, 准教授 (10271090)
• Co-Investigator(Renkei-kenkyūsha): Mochizuki Takuro 京都大学, 数理解析研究所, 教授 (10315971)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 非可換代数幾何学 / 非可換環論 / ワイル環

Outline of Final Research Achievements

Regarding non-commutative algebraic geometry, we can apply ordinary algebraic geometry method by understanding through reduction to the positive characteristics. We organized the geometric problems, raised one way of thinking about the definition itself and regularity of non-commutative varieties.
I defined the non-commutative projective space and a version of the theory of differential forms on it, and set the pathway of calculating its cohomology.

Free Research Field

代数学