derived Gabriel topology and its applications

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610009
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Osaka Prefecture University
• Principal Investigator: Minamoto Hiroyuki 大阪府立大学, 理学(系)研究科(研究院), 准教授 (50527885)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ホモロジー代数 / 導来圏 / 微分次数付圏

Outline of Final Research Achievements

A ring R is a system of numbers which admits addition, subtraction and multiplication and that an R-module is a module which admits an action of R. Studying relationship between R-modules via homological algebra, requires enlarge rings into differential graded(DG) rings. In this project, I had studied basic theory of DG-rings. I found that a basic property of commutator rings does not hold for DG commutator rings. I introduced universal localization for DG-rings and applied it to classification problem of thick subcategories of the derived category of a ring.I computed Massey products on Yoneda algebra in terms of extensions of the modules and, as an application, gave a clear proof and generalization of Gugenheim-May Theorem. I showed that DG-Frobenius algebra possesses an A-infinity Nakayama automorphism.

Free Research Field

代数学