IMPROPER INTERSECTIONS OF KUDLA–RAPOPORT DIVISORS AND EISENSTEIN SERIES
IMPROPER INTERSECTIONS OF KUDLA–RAPOPORT DIVISORS AND EISENSTEIN SERIES
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KUDLA–RAPOPORT 因子与艾森斯坦级数的不当交集
DOI：
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发表时间：
2014
影响因子：
0.9
通讯作者：
Siddarth Sankaran
中科院分区：
文献类型：
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作者：
Siddarth Sankaran
我们考虑了一族Kudla-Rapoport循环，该循环位于签名(1，1)的酉群上的Shimura簇的积分模型上，并且证明了这些循环的算术次数是亏格2的Eisenstein级数的中心导数的傅里叶系数。所讨论的积分模型将具有非主极化和虚二次数环的作用的阿贝尔曲面参数化，在这种情况下，这些循环是退化的：它们可以包含正的维分量。这一结果可以看作是对Kudla猜想和Kudla-Rapoport猜想的印证，这些猜想预言了特殊圈的交数与自同构形的傅里叶系数之间的关系。
We consider a certain family of Kudla–Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1, 1), and prove that the arithmetic degrees of these cycles are Fourier coefficients of the central derivative of an Eisenstein series of genus 2. The integral model in question parameterizes abelian surfaces equipped with a non-principal polarization and an action of an imaginary quadratic number ring, and in this setting the cycles are degenerate: they may contain components of positive dimension. This result can be viewed as confirmation, in the degenerate setting and for dimension 2, of conjectures of Kudla and Kudla–Rapoport that predict relations between the intersection numbers of special cycles and the Fourier coefficients of automorphic forms.
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