论文标题
Krämer模型的Kudla-Ropoport猜想
Kudla-Rapoport conjecture for Krämer models
论文作者
论文摘要
在本文中，我们提出了一个改良的库德拉·里波特（Kudla-Ropoport）猜想，该猜想是针对ramifiend prime的统一rapoport-zink空间的Krämer模型的，这是一个精确的身份，将特殊周期的交点与Hermitian局部密度多项式的衍生物相关。我们还介绍了特殊差异周期的概念，该周期具有令人惊讶的简单描述。将其与遗传学局部密度多项式的感应公式相结合，我们证明了经过修改的kudla-roport猜想时，当$ n = 3 $时。我们的猜想与惰性和无限素数的已知结果结合在一起，意味着当相应的单一shimura品种的水平结构由自二个lattice定义时，对于所有非单明系数的算术siegel-weil公式。
In this paper, we propose a modified Kudla-Rapoport conjecture for the Krämer model of unitary Rapoport-Zink space at a ramified prime, which is a precise identity relating intersection numbers of special cycles to derivatives of Hermitian local density polynomials. We also introduce the notion of special difference cycles, which has surprisingly simple description. Combining this with induction formulas of Hermitian local density polynomials, we prove the modified Kudla-Rapoport conjecture when $n=3$. Our conjecture, combining with known results at inert and infinite primes, implies arithmetic Siegel-Weil formula for all non-singular coefficients when the level structure of the corresponding unitary Shimura variety is defined by a self-dual lattice.
