Representation theory of Iwanaga-Gorenstein rings from the viewpont of tilting thoery
| Project/Area Number |
26800007
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | University of Yamanashi |
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Principal Investigator |
YAMAURA Kota 山梨大学, 大学院総合研究部, 助教 (60633245)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 岩永-Gorenstein環 / Cohen-Macaulay加群 / 三角圏 / 傾理論 / 傾対象 / 安定圏 |
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| Outline of Final Research Achievements |
The purpose is to study the stable category of graded Cohen-Macaulay modules over graded Iwanaga-Gorenstein rings from the viewpoint of tilting theory. We have the following results.
1. For a one dimensional graded commutative Gorenstein ring A with some assumptions, the thick subcategory generated by the syzygies of graded simple modules in the stable category of graded Cohen-Macaulay A-modules has a silting object. Moreover, the thick subcategory has a tilting object if and only if either A is regular or the a-invariant of A is non-negative.
2. Let R be an algebra over a filed and C be a bimodule. Assume that the trivial extension A of R by C is Iwanaga-Gorenstein. Then the stable category of graded Cohen-Macaulay A-modules can be realized as an admissible subcategory of the bounded derived category of the category of finitely generated R-modules if the global dimension of R is finite.
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Report
(5 results)
Research Products
(4 results)
