Research on the stable homotopy category using quasi-categories
Project/Area Number |
25400092
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Okayama University |
Principal Investigator |
Torii Takeshi 岡山大学, 自然科学研究科, 准教授 (30341407)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 安定ホモトピー圏 / quasi-category / モデル圏 / Bousfield局所化 / 導来圏 / 表現のモジュライ / Morava K理論 / 安定ホモトピー論 / スペクトラム / Morava K理論 / Bousfiled局所化 / Johnson-Wilson理論 / 離散Gスペクトラム / Morava E理論 / 降下スペクトル系列 / ホモトピー論的代数幾何 / クロマティックホモトピー論 / ホモトピー固定点スペクトラム / Bousfield 局所化 / Lubin-Tate コホモロジー / クロマティックホモトピー理論 / Lubin-Tateコホモロジー |
Outline of Final Research Achievements |
I have studied the stable homotopy category and its localizations by means of quasi-categories. Through spectral sequences, the stable homotopy category and its Bousfield localizations are considered to be related to the categories of representations for some groups and their derived categories. I gave a formulation of this relationship through the theories of model categories and quasi-categories. I have also constructed a functor between algebraic models of Bousfield localizations of the stable homotopy category via Morava K-theories. Furthermore, based on these, I have also studied more general moduli spaces of representations.
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Report
(5 results)
Research Products
(15 results)