论文标题
零循环中的零循环的过滤在阿贝里亚品种和同等基因下的行为
Filtrations of the Chow group of zero-cycles on abelian varieties and behavior under isogeny
论文作者
论文摘要
对于\ cite {gazaki2015}的作者定义的abelian品种$ a $ a $ a $ a $ a $ a $ $ k $ -group。在本文中，我们表明，这种过滤在同学方面表现良好，特别是如果$ n：a \ to $ a $是$ a $上的$ n $ map的乘法，则在$ a $上的$ n $ map，然后在商$ f^r/f^r/f^{r+1} $上通过乘以$ n^r $在$ f^r/f^r/f^r/f^r+1} $上给出其推送$ n_ \ star $。在特殊情况下，当$ a = e_1 \ times \ cdots \ times e_d $是椭圆曲线的产物时，我们表明这种过滤与Raskind和Spiess定义的过滤一致，以及Beauville和Beauville和Bloch先前考虑的Pontryagin Filtration。当$ a $对椭圆曲线的产物不同步时，我们还会在更一般的情况下获得一些结果。当$ k $是$ \ mathbb {q} _p $的有限扩展时，使用对椭圆曲线产品不相关的曲线的jacobians，我们为猜想的Raskind和spiess和spiess and colliot-thélène提供了新的证据，这预测了Albanese Map of Albanese Map of Albanese Map of Albanese Map的直接总和是一个划分的组和一个有限的组和一个有限的组。
For an abelian variety $A$ over a field $k$ the author defined in \cite{Gazaki2015} a Bloch-Beilinson type filtration $\{F^r(A)\}_{r\geq 0}$ of the Chow group of zero-cycles, $\text{CH}_0(A)$, with successive quotients related to a Somekawa $K$-group. In this article we show that this filtration behaves well with respect to isogeny, and in particular if $n:A\to A$ is the multiplication by $n$ map on $A$, then its push-forward $n_\star$ is given on the quotient $F^r/F^{r+1}$ by multiplication by $n^r$. In the special case when $A=E_1\times\cdots\times E_d$ is a product of elliptic curves, we show that this filtration agrees with a filtration defined by Raskind and Spiess and with the Pontryagin filtration previously considered by Beauville and Bloch. We also obtain some results in the more general case when $A$ is isogenous to a product of elliptic curves. When $k$ is a finite extension of $\mathbb{Q}_p$, using Jacobians of curves isogenous to products of elliptic curves, we give new evidence for a conjecture of Raskind and Spiess and Colliot-Thélène, which predicts that the kernel of the Albanese map is the direct sum of a divisible group and a finite group.
