motivic cohomology and classifying spaces
| Project/Area Number |
17540007
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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 | Ibaraki University |
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Principal Investigator |
YAGITA Nobuaki Ibaraki University, College of Education, professor (20130768)
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| Co-Investigator(Kenkyū-buntansha) |
OKAYASU Takashi Ibaraki University, College of Education, Associate professor (00191958)
KUDOU Kenji Ibaraki University, College of Education, Lecturer (00114017)
KANEDA Massaharu Osaka City University, Faculty of Science, professor (60204575)
TEZUKA Michishige Rykyus University, Faculty of Science, professor (20197784)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,540,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | motvic cohomology / classifying space / BP-theory / motivic cohomology / algebraic cobordism / Pfister quadric / コンプレックスコボルディズム / 代数的コボルディズム |
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| Research Abstract |
A Suslin and V. Voevodsky constructed and developed the motivic cohomology theory H^{*, *''} (X; Z/p) for algebraic sets X over the base field k. This theory is the counter part in algebraic geometry of the usual mod p singular cohomology in algebraic topology. Let ch (k)=0 and fix an embedding that k is subset C. As the counter part of the complex cobordism theory MU^* (X), Voevodsky defined the algebraic cobordism theory MGL^{*, *''} (X) and used it in the first proof of the Milnor Conjecture. Given a nonzero symbol a in K_{n+1}^M (k)/p, the norm variety V_a is a variety such that a=0 in K_{n+1}^M (k (V_a))/p and V_a c=v_n. Here v_n is the 2 (p^n-1) complex manifold generating the coefficient ring of the BP-theory in algebraic topology. In these papers we write down the properties of ABP^{*, *''} (X) which is the algebraic counter part of BP-theory. For example we give a construction of the Atiyah-Hirzebruch spectral sequence for ABP^{*, *} (X; \bZ/p); its existence (of$MGL$-version) was announced by Hopkins and Morel more that several years before, however any proof (or even statement), does not appear yet. We study the cohomology operations, products and Gysin maps explicitly in $ABP^{*, *''}$-theory.
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Report
(4 results)
Research Products
(15 results)
