论文标题
Chow群体和$ L $衍生的自动形态动机
Chow groups and $L$-derivatives of automorphic motives for unitary groups
论文作者
论文摘要
在本文中，我们研究了与一个与CM扩展相关的统一组的钢化$ l $ -l $π$π$相关的动机的Chow Group，其全球根号为$ -1 $。我们表明，在对$π$的后果的一些限制下，如果中央衍生物$ l'（1/2，π）$是不变的，则$π$ near-nearly同种型本地化，其在其反射场中的某个统一shimura品种的食物组不会消失。这证明了Beilinson的一部分 - Chow群体和$ L $ functions的Bloch猜想，这概括了Birch和Swinnerton-Dyer的猜想。此外，假设库德拉（Kudla）生成的特殊周期功能的模块化，我们通过算术theta的提升将Chow Group的一定$π$ - nearly Isotypic子空间明确构建，并以中央衍生物$ l'（1/2，π）$和local local doubled zeta集成ZETA的中央衍生产品高度。这证实了我们一个人提出的猜想算术内产物公式，该公式将大的Zagier公式推广到更高的维动机。
In this article, we study the Chow group of the motive associated to a tempered global $L$-packet $π$ of unitary groups of even rank with respect to a CM extension, whose global root number is $-1$. We show that, under some restrictions on the ramification of $π$, if the central derivative $L'(1/2,π)$ is nonvanishing, then the $π$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and $L$-functions, which generalizes the Birch and Swinnerton-Dyer conjecture. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $π$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,π)$ and local doubling zeta integrals. This confirms the conjectural arithmetic inner product formula proposed by one of us, which generalizes the Gross--Zagier formula to higher dimensional motives.
