Rational structure of X(N) over ℚ and explicit Galois action on CM points

Abstract

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.

Keywords

Siegel modular variety / Galois action / Explicit reciprocity law

References

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