Study on the Picard groups of stable homotopy categories
| Project/Area Number |
26400092
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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 |
Geometry
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| Research Institution | Kochi University |
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Principal Investigator |
Shimomura Katsumi 高知大学, 教育研究部自然科学系理学部門, 教授 (30206247)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Hopkinｓ’Picard group / 安定ホモトピー圏 / Morava K-theory / Johnson-Wilson spectrum / Adams スペクトル系列 / Hopkin's Picard group / ピカール群 / MoravaのK理論 / Johnson-Wilsonのスペクトラム / Adamsスペクトル系列 |
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| Outline of Final Research Achievements |
The stable homotopy category of spectra is understood by the stable homotopy categories K_n of spectra localized by the Morava K-theoreis K(n) for a non-negative integers n. To determine the Hopkins' Picard group of K_n is one of important problems in the stable homotopy theory. Our aim of this study is to consider the Picard groups not by the Morava K-theories, but by the Johnson-Wilson spectrum E(n). One of our main results is that the subgroup of the Picard group of K_n obtained by a geometric consideration is isomorphic to the counterpart of the Picard group of the stable homotopy category localized by E(n), under a condition.
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Report
(4 results)
Research Products
(14 results)
