Derived geometry and duality
| Project/Area Number |
25800001
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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 | Tohoku University |
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Principal Investigator |
Iwanari Isamu 東北大学, 理学研究科, 准教授 (70532547)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 淡中双対 / 高次圏 / モチーフ / DG代数 / 変形理論 / 有理ホモトピー / 基本群 / 安定∞圏 / 周期写像 / 導来代数幾何学 / 混合モチーフ / オペラッド / ガロア群 |
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| Outline of Final Research Achievements |
The principal purpose of this program is to study a duality of tannakian type for higher categories and to apply it to various theory such as mixed motives. I proved a tannakian characterization theorem for symmetric monoidal stable infinity-categories that satisfy a certain simple condition (so-called fine tannakian infinity-categories). I applied this theory to mixed motives to obtain motivic Galois stacks and associated motivic Galois group. I also define a motivic rational homotopy type and its relation with motivic Galois actions and related notions. I applied the tannaka duality theory to motivic rational homotopy types.
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Report
(5 results)
Research Products
(21 results)
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[Presentation] ∞圏についてのレクチャー2015
Author(s)
岩成勇
Organizer
第三回代数トポロジー信州春の学校
Place of Presentation
信州大学理学部 （松本市）
Year and Date
2015-03-03 – 2015-03-06
Related Report
Invited
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