志村曲線在西格爾模三維流型上的映射

Abstract

在這篇論文中，我們首先計算在西格爾模三維流型上有幾個不同的志村曲線的映射。接著我們用特定志村曲線的Hauptmodul來參數化表示這些虧格為０的像。

Let O be a maximal order in an indefinite quaternion algebra of discriminant D over Q and Q_D be the set of points in Siegel’s modular threefold A_2 whose corresponding abelian surfaces have quaternionic multiplication by O. In this thesis, we first determine the number of irreducibe components in Q_D and then for each irreducible component of genus 0, we will find a parameterization in terms of the Hauptmodul of a certain Shimura curve associated to O.