佐賀大学理工学部
第163回応数談話会

日時

2002年12月12日 (木曜日) 16:00-17:00

講演者

Henri Darmon 氏(McGill Univ. 数学)

題目

Elliptic curves and Hilbert's twelfth Problem II

要旨

Hilbert's twelfth problem is concerned with constructing class fields of a number field K by transcendental means. A prototype of what is sought for is the theory of complex multiplication, allowing the construction of abelian extensions of an imaginary quadratic field K by evaluating elliptic modular functions at arguments in K. In the 1960's Stark proposed a conjectural solution to Hilbert's twelfth problem for a larger class of number fields (including totally real fields), predicting the existence of special units in these extensions constructed from derivatives of abelian L-series at s=0. It has also been observed for some time that there is a special resonance between the problem of constructing units in number fields and rational points on elliptic curves. I will report on an emerging conjectural picture which allows the construction of algebraic points on elliptic curves in terms of periods of the associated modular forms. This picture is a generalisation of the theory of complex multiplication, and any progress on it would yield new insights into two important questions in number theory: the construction of class fields, and of rational points on elliptic curves.

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＠]
FAX 0952-28-8501　TEL 0952-28-8521