On Brumer’s family of RM-curves of genus two

Ki Ichiro Hashimoto*

*この研究の対応する著者

研究成果: Article査読

13 被引用数 (Scopus)

抄録

We reconstruct Brumer’s family with 3-parameters of curves of genus two whose jacobian varieties admit a real multiplication of discriminant 5. Our method is based on the descent theory in geometric Galois theory which can be compared with a classical problem of Noether. Namely, we first construct a 3-parameter family of polynomials f(X) of degree 6 whose Galois group is isomorphic to the alternating group A5. Then we study the family of curves defined by Y2 = f(X), showing that they are equivalent to Brumer's family. The real multiplication will be described in three distinct ways, i.e., by Humbert's modular equation, by Poncelet's pentagon, and by algebraic correspondences.

本文言語English
ページ(範囲)475-488
ページ数14
ジャーナルTohoku Mathematical Journal
52
4
DOI
出版ステータスPublished - 2000
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「On Brumer’s family of RM-curves of genus two」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル