2012 Fiscal Year Final Research Report
Toward Derived Tannaka duality
| Project/Area Number |
23840003
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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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, 大学院・理学研究科, 准教授 (70532547)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 導来代数幾何 / 双対性 / ホモトピー / 高次圏 / モチーフ |
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| Research Abstract |
In 2011-2012, we obtained several results concerning tannaka duality type theorems towards applications to mixed motives. Some results are purely categorical and derived algebraid theoretic, and others are about motives. One algebraic powerful machinery I constructed is tannakization in the realm of derived algebraic geometry. Applying it to motivic situations we constructed derived and underived motivic Galois groups. Moreover, I found a refined tannaka duality type theorem which are well-suited to motivic applications and studied the structure of motivic Galois groups for the cases where one cannot use techniques in mixed Tate motives .
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