AI 中文总结
该研究探讨有理乘N映射在特定阿贝尔簇退化周环群上的作用，结合傅里叶变换，计算单位截面类、证明相对周动机广义权分解并确定重言环，属代数几何领域的相关研究。
AI 中文摘要
我们研究有理乘N映射在环秩至多为1的主极化阿贝尔簇退化的周环群上的作用，及其与傅里叶变换的相互作用。作为应用，我们计算单位截面的类，证明此类退化泛族的相对周动机的广义权分解，并完全确定其重言环。
英文摘要
We study the action of the rational multiplication by $N$ map on the Chow groups of degenerations of principally polarized abelian varieties of torus rank at most one, as well as its interaction with the Fourier transform. As applications, we compute the class of the unit section, prove a generalized weight decomposition of the relative Chow motive of the universal family of such degenerations, and completely determine its tautological ring.
Comments100 pages, 8 figures
