Journal of University of Chinese Academy of Sciences >
On the K2 group of a family of curves
Received date: 2008-01-29
Revised date: 2008-05-15
Online published: 2009-03-15
Supported by
supported by the National Natural Science Foundation of China (10671202) and Hundred Talent program of Chinese Academy of Sciences corresponding author
In this paper, we construct a family of algebraic curves over Q with many elements in the K2 group. Some interesting linear relationships between these elements are proved. Moreover, the integrality property of these elements is discussed.
Key words： algebraic curve; Beilinson’s conjecture; K2 group; torsion divisor
LIU Hang , TANG Guo-Ping . On the K2 group of a family of curves[J]. Journal of University of Chinese Academy of Sciences, 2009 , 26(2) : 152 -157 . DOI: 10.7523/j.issn.2095-6134.2009.2.002
[1] Schneider P. Introduction to the Beilinson conjectures. In: Rapoport M, Schappacher N, Schneider P.(ed.) Beilinson's Conjectures on Special Values of L-Functions. Boston: Academic Press, 1988. 1~35
[2] Dokchitser T, de Jeu R, Zagier D. Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves. Compositio Mathematica, 2006, 142(2): 339~373
[3] Rosenberg J. Algebraic K-theory and its applications. New York: Springer-Verlag, 1994
[4] Silverman J. Advanced topics in the arithmetic of elliptic curves. New York: Springer-Verlag, 1994
[5] Liu Q. Algebraic geometry and arithmetic curves. Oxford: Oxford University Press, 2002
/
| 〈 |
|
〉 |