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Resolution of singularities of defining equations of number field and its relation to zeta function

Research Project

Project/Area Number 22654003
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

MAEDA Hironobu  東京農工大学, 大学院・工学研究院, 准教授 (50173711)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥1,280,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2010: ¥500,000 (Direct Cost: ¥500,000)
Keywords代数体 / 特異点 / 底式 / 定義方程式 / 実射影平面 / 2次形式 / 判別式 / 単位元形式 / 特異点集合 / 代数的整数論 / 特異点解消 / ゼータ関数
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.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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