论文标题
零周期的划分结果
Divisibility Results for zero-cycles
论文作者
论文摘要
令$ x $成为有限的未受到扩展$ k $ $ \ mathbb {q} _p $的光滑投射曲线的产品。假设$ x $的阿尔巴尼斯品种具有很好的减少，并且$ x $具有$ k $ - 理性点。我们提出以下猜想。 Albanese Map的内核$ CH_0（x）^0 \ rightArrow \ text {alb} _x（k）$ is $ p $ - 数字。当$ p $是一个奇怪的素数时，我们证明了大型椭圆曲线产品和某些主要均匀品种的猜想。使用此情况，我们提供了一些证据证明了Colliot-Thélène和Sansuc零循环（\ cite {colliot-thelene/sansuc1981}）的零循环的局部到全球猜想，以及Kato and Saito（\ cite {kato/saito1986}）。
Let $X$ be a product of smooth projective curves over a finite unramified extension $k$ of $\mathbb{Q}_p$. Suppose that the Albanese variety of $X$ has good reduction and that $X$ has a $k$-rational point. We propose the following conjecture. The kernel of the Albanese map $CH_0(X)^0\rightarrow\text{Alb}_X(k)$ is $p$-divisible. When $p$ is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (\cite{Colliot-Thelene/Sansuc1981}), and Kato and Saito (\cite{Kato/Saito1986}).
