论文标题
算术特殊周期和雅各比形式
Arithmetic special cycles and Jacobi forms
论文作者
论文摘要
我们认为，库德拉（Kudla）引入的特殊周期的家族在完全真实领域的各向异性二次空间上的shimura品种上。通过用绿色电流增强这些周期，我们在这些Shimura品种的规范模型的算术小组中获得类（视为其反射场上的算术品种）。本文的主要结果断言，可以通过非形态Hilbert-Jacobi模块化形式的傅立叶扩展来识别从这些周期构建的产生序列。该结果为库德拉（Kudla）猜想的算术类似物提供了证据，该猜想将这些周期与西格尔模块化形式有关。
We consider families of special cycles, as introduced by Kudla, on Shimura varieties attached to anisotropic quadratic spaces over totally real fields. By augmenting these cycles with Green currents, we obtain classes in the arithmetic Chow groups of the canonical models of these Shimura varieties (viewed as arithmetic varieties over their reflex fields). The main result of this paper asserts that generating series built from these cycles can be identified with the Fourier expansions of non-holomorphic Hilbert-Jacobi modular forms. This result provides evidence for an arithmetic analogue of Kudla's conjecture relating these cycles to Siegel modular forms.
