標題: 志村曲線在西格爾模三維流型上的映射
Quaternionic loci in Siegel’s modular threefold
作者: 林易萱
楊一帆
Lin, Yi-Hsuan
Yang, Yi-fan
應用數學系所
關鍵字: 西格爾模三維流型;志村曲線;QM;abelian surface;Shimura curve;Siegel's modular threefold
公開日期: 2016
摘要: 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.
URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070082201
http://hdl.handle.net/11536/140376
Appears in Collections:Thesis