2012 Fiscal Year Final Research Report
Chromatic redshift and homotopical algebraic geometry
| Project/Area Number |
22540087
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Okayama University |
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Principal Investigator |
TORII Takeshi 岡山大学, 大学院・自然科学研究科, 准教授 (30341407)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 安定ホモトピー圏 / クロマティック赤方偏移 / ホモトピー論的代数幾何 / ホモトピー固定点スペクトラム / Adamsスペクトル系列 / HKR指標 / Morava E理論 / Chern指標 |
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| Research Abstract |
I studied the relationship among the layers of the chromatic filtration in the stable homotopy category bymeans of homotopical algebraic geometry. I obtained the relationship between the Hecke operators on the Morava E-theories with different heights. I also showed that any spectrum which is local with respect to the Morava K-theory can be obtained as the homotopy fixed point spectrum for its Morava module in collaboration with D.G.Davis. Furthermore, I obtained results on the embeddings of the module categories for the Galois extensions of commutative S-algebras.
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