Intersections of special cycles on the Shimura variety for
Intersections of special cycles on the Shimura variety for
复制标题
志村品种的特殊周期的交叉点
DOI：
10.1515/crelle-2011-0006
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Ulrich Terstiege
中科院分区：
文献类型：
--
作者：
Ulrich Terstiege
我们建立了GU（1，2）的Shimura簇算术模型上特殊圈的交重数与某些非相干Eisenstein级数导数的Fourier系数之间的密切联系，证实了Kudla和Rapoport的一个猜想.本文分为两个部分。第一部分是本文的主体部分，研究了p-可除群的模空间上的局部特殊圈的交。这种模空间的p-可分群可用于完成志村品种沿着超奇异轨迹的纤维在一个惰性素数p的均匀化。我们调查的结构，当地的特殊周期和它们的交叉点。特别地，我们给出了一个明确的描述的特殊纤维的局部特殊循环。然后，我们证明了一个明确的公式的交叉多重性的三个局部特殊的循环，并将其与某些厄米表示密度，也证实了一个猜想的库德拉和Rapoport。为此，我们还给出了相关厄米表示密度\alpha_p（1_s，T）的显式归纳公式，其中T的形式为diag（p^{a_1}，.，p^{a_n}）。在第二部分中，我们应用第一部分的主要结果证明了（整体）特殊圈的交重数与Eisenstein级数导数的Fourier系数之间的关系。
We establish a close connection between intersection multiplicities of special cycles on arithmetic models of the Shimura variety for GU(1,2) and Fourier coefficients of derivatives of certain incoherent Eisenstein series, confirming a conjecture of Kudla and Rapoport. The paper is divided into two parts. The first part is the bulk of the paper and investigates intersections of local special cycles which are defined on a certain moduli space of p-divisible groups. This moduli space of p-divisible groups can be used for the uniformization of the completion of the Shimura variety along the supersingular locus in the fiber at an inert prime p. We investigate the structure of local special cycles and of their intersections. In particular, we give an explicit description of the special fiber of a local special cycle. We then prove an explicit formula for the intersection multiplicity of three local special cycles and relate it to certain hermitian representation densities, also confirming a conjecture of Kudla and Rapoport. To this end, we also give an explicit inductive formula for the relevant hermitian representation densities \alpha_p(1_s,T), where T is of the form diag(p^{a_1},...,p^{a_n}). In the second part, we apply the main result of the first part to prove the relation of intersection multiplicities of (global) special cycles and Fourier coefficients of derivatives of Eisenstein series.
单一志村品种的特殊周期 I 无分支的当地理论
影响因子：
3.1
作者：
S. Kudla;M. Rapoport
通讯作者：
M. Rapoport