標題: | Quaternionic loci in Siegel's modular threefold |
作者: | Lin, Yi-Hsuan Yang, Yifan 應用數學系 Department of Applied Mathematics |
關鍵字: | Primary 11G15;Secondary 11F03;11F46;11G10 |
公開日期: | 1-六月-2020 |
摘要: | Let QD be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order O in an indefinite quaternion algebra of discriminant D over Q such that the Rosati involution coincides with a positive involution of the form alpha & x21a6;mu-1 alpha over bar mu on O for some mu is an element of O with mu 2+D=0. In this paper, we first give a formula for the number of irreducible components in QD, strengthening an earlier result of Rotger. Then for each irreducible component of genus 0, we determine its rational parameterization in terms of a Hauptmodul of the associated Shimura curve. |
URI: | http://dx.doi.org/10.1007/s00209-019-02372-z http://hdl.handle.net/11536/154554 |
ISSN: | 0025-5874 |
DOI: | 10.1007/s00209-019-02372-z |
期刊: | MATHEMATISCHE ZEITSCHRIFT |
Volume: | 295 |
Issue: | 1-2 |
起始頁: | 775 |
結束頁: | 819 |
顯示於類別: | 期刊論文 |