2011 Fiscal Year Final Research Report
Conservativity and finite dimensional conjecture for Motives
| Project/Area Number |
21540038
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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 |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Nobuyoshi 広島大学, 大学院・理学研究科, 准教授 (60301298)
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| Project Period (FY) |
2009 – 2011
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| Keywords | チャウ多様体 / トーリック多様体 / モチビックチャウ級数 / モチーフ / 有限次元性予想 |
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| Research Abstract |
Algebraic varieties are the spaces defined as the zero sets of polynomials. Closed sub algebraic varieties are parametrized also by algebraic varieties, called Chow varieties. The main result of this research is that the power series taking these Chow varieties(of important varieties such as Toric varieties) as coefficients become rational functions, under the relation called A^1 homotopy. A^1 homotopy naturally arises in non-commutative motives, related to physical mathematics, and our result implies that Chow varieties must be deeply related to physical mathematics.
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