Shimura curves embedded in Igusa's threefold
Victor Rotger
Abstract
Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus QO of quaternionic multiplication by O in the moduli space Ag of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe QO as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of QO in terms of class numbers of CM-fields.
Create a lesson
Related papers
An ergodic approach to equations of the form x+y=α(n)
Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín
Rogers--Ramanujan identities from the geometry of Xa=Yb
Yifeng Huang, Kenny Lau, Ken Ono
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
Jean-Marc Sac-Épée, Souad El Otmani, Armand Maul et al.
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
A problem of Yang and Chen on weighted representation functions
Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan