This paper reviews a less known rational structure on the Siegel modular variety X(N) = Γ(N)\H_g over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety....This paper reviews a less known rational structure on the Siegel modular variety X(N) = Γ(N)\H_g over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.展开更多
基金supported by the National Science Foundation Grants(No.DMS-1200380,DMS-1500743)the Chinese Qian Ren Plan of Tsinghua(No.543100001)
文摘This paper reviews a less known rational structure on the Siegel modular variety X(N) = Γ(N)\H_g over Q for integers g, N ≥ 1. The author then describes explicitly how Galois groups act on CM points on this variety. Finally, another proof of the Shimura reciprocity law by using the result and the q-expansion principle is given.
