论文标题
精制的高度配对
Refined height pairing
论文作者
论文摘要
对于$ d $维平滑的光滑投射品种$ x $，优于平稳品种$ b $上的$ k $，而对于$ i \ ge 0 $，我们定义了$ ch^i（x）$的子组$ ch^i（x）^{（0）} $ ch^{d+1-i}（x）^{（0）} \ to ch^1（b）\]在Abelian组的类别中，模拟降低。对于$ i = 1，d $，$ ch^i（x）^{（0）} $是数值等同于$ 0 $的循环的组。这种配对与P. Schneider和A. Beilinson定义的配对有关，如果$ b $是一条曲线，当$ x $是Abelian的品种时，L. Moret-Bailly定义了高度，并且与$ h^2中的值配对（b _ {\ bar k}，\ bar k}，\ nathbf {q} _ {q} _l（1） 一般的。当$ i = 1 $时，我们会详细研究它。
For a $d$-dimensional smooth projective variety $X$ over the function field of a smooth variety $B$ over a field $k$ and for $i\ge 0$, we define a subgroup $CH^i(X)^{(0)}$ of $CH^i(X)$ and construct a "refined height pairing" \[CH^i(X)^{(0)}\times CH^{d+1-i}(X)^{(0)}\to CH^1(B)\] in the category of abelian groups modulo isogeny. For $i=1,d$, $CH^i(X)^{(0)}$ is the group of cycles numerically equivalent to $0$. This pairing relates to pairings defined by P. Schneider and A. Beilinson if $B$ is a curve, to a refined height defined by L. Moret-Bailly when $X$ is an abelian variety, and to a pairing with values in $H^2(B_{\bar k},\mathbf{Q}_l(1))$ defined by D. Rössler and T. Szamuely in general. We study it in detail when $i=1$.
