rationality problem on extension fields
| Project/Area Number |
24540019
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
YAMASAKI Aiichi 京都大学, 理学(系)研究科(研究院), 准教授 (10283590)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | rationality problem / algebraic torus / conic bundle / Noether's problem / unramified cohomology / relation module / Bravais群 / 有理性問題 / Noether問題 / 有限群 |
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| Outline of Final Research Achievements |
Let X be an affine surface defined by the equation z^2=P(x)y^2+Q(x). The rationality problem of X has been solved in terms of the polynomials P(x) and Q(x).
The rationality problems of algebraic torus has been solved up to dimension 5. Rationality problems for algebraic tori of dimension 3 was determined by Kunyavskii. But as for algebraic tori of dimension 4 and 5, rationality problems were solved only for special cases.
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Report
(4 results)
Research Products
(15 results)
