佐賀大学理工学部
第150回応数談話会

日時

2000年10月 5日 （木曜日） 16:00--17:30

講演者

Reinhard Schertz 氏 （アオグスブルク大学）

題目

Problems of Construction in Complex Multiplication

要旨

Let Q_f be the f-th cyclotomic field and O_f its ring of integers. Then it is well known that

O_f = Z[ζ], ζ = e^{2π i/f}.

This means that O_f can be described by torsion points of the unit circle x² + y² = 1.
Now let K = Q(√d), d < 0, be a quadratic imaginary number field and H its Hilbert class field. For an integral ideal f in K we consider the ray class field K_f of K. From complex multiplication we know that K_f can be constructed over H by torsion points of elliptic curves.
It is the aim of this talk to show that in analogy to the cyclotomic case the ring of integers of K_f has an integral basis over the ring of integers of H which is constructed from torsion points of an elliptic curve. In almost all cases the basis obtained in this way is a power basis.

場所

数理科学科大セミナー室（理工学部ＤＣ棟５階５０１）

連絡先

〒840-8502 佐賀市本庄町１ 佐賀大学理工学部数理科学科
中原 徹 [nakahara＠]
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