2016 Fiscal Year Final Research Report
Gorenstein dimension in Derived categories
| Project/Area Number |
26400036
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Research Collaborator |
KAMEYAMA Noritsugu サレジオ工業高等専門学校, 一般教育科, 助教 (00780024)
KOGA Hirotaka 東京電機大学, 情報環境学部, 助教 (30736723)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 導来圏 / ゴレンシュタイン次元 / アウスランダー・ゴレンシュタイン環 / フロベニウス拡大 |
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| Outline of Final Research Achievements |
Let A be an abelian category with enough projectives, P the full subcategory of A consisting of projective objects, and G the full subcategory of A consisting of Gorenstein projective objects.In this setting, we showed that a bounded complex X over A has finite Gorenstein dimension if and only if X is isomorphic to some bounded complex over G in the derived category of bounded complexes over A, that in the derived category of bounded complexes over A the full subcategory consisting of complexes of finite Gorenstein dimension is really a triangulated category, and that the residue category of G over P is equivalent to the quotient category of the triangulated category of chain complexes of finite Gorenstein dimension over the triangulated subcategory of chain complexes of finite projective dimension.
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| Free Research Field |
代数学
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