| Project/Area Number |
26610010
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Ube National College of Technology |
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Principal Investigator |
Kato Yuki 宇部工業高等専門学校, 一般科, 講師 (50707130)
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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 |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 数論幾何学 / モデル圏 / 代数的K-理論 / A1ホモトピー論 / 導来代数幾何学 / A^1ホモトピー理論 / 代数的K‐理論 / 代数的コボルディズム / ボット周期性 / 代数的K理論 / A1-ホモトピー理論 |
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| Outline of Final Research Achievements |
We established the theory of motivic derived algebraic geometry for left proper combinatorial simlicial model categories. In the framework of motivic derived algebraic geometry, we can construct of the motivic version of derived schemes and stacks by using motivic versions of infinity-categories. For example, we can obtain the moduli stacks of vector bundles and Thom spaces on motivic schemes. These results give us examples of applications of motivic derived algebraic geometry to moduli problems. We wrote the research the article "Motivic model categories and motivic derived algebraic geometry".
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