2012 Fiscal Year Final Research Report
Resolution of singularities of defining equations of number field and its relation to zeta function
| Project/Area Number |
22654003
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Agriculture and Technology |
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Principal Investigator |
MAEDA Hironobu 東京農工大学, 大学院・工学研究院, 准教授 (50173711)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 代数体 / 特異点 / 底式 / 定義方程式 |
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| Research Abstract |
The defining equation of a number field is not unique and has in general many singular and infinitely near singular points. One can read some number theoretic properties, e.g. prime ideal decomposition, from these singularities, but we cannot find any properties of singutlarities, which distinguishes real and imaginary extensions. On the other hand I was able to prove the singular locus of the fundamental equation of a number field is contained in the zero points of a homogeneous form, which Hilbert called the Einheitsform in his Zahlbericht.
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