论文标题
家庭中椭圆曲线产品的理性等价
Rational Equivalences on Products of Elliptic Curves in a Family
论文作者
论文摘要
Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson predicts that the image of this map is当$ k $是一个数字字段时，有限。我们构建了一个$ 2 $ - 参数椭圆曲线家族，可用于生成对$ e_1，e_2 $的示例，而该图像是有限的。该家庭的构建是为了确保存在通过$ e_1 \ times e_2 $的Kummer表面中指定点的有理曲线。
Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson predicts that the image of this map is finite when $k$ is a number field. We construct a $2$-parameter family of elliptic curves that can be used to produce examples of pairs $E_1,E_2$ where this image is finite. The family is constructed to guarantee the existence of a rational curve passing through a specified point in the Kummer surface of $E_1\times E_2$.
