Finite Flatness of Torsion Subschemes of Hilbert-Blumenthal Abelian Varieties

Let E be a totally real number field of degree d over Q. We give a method for constructing a set of Hilbert modular cuspforms f1, . . . , fd with the following property. Let K be the fraction field of a complete dvr A, and let X/K be a Hilbert-Blumenthal abelian variety with multiplicative reduction and real multiplication by the ring of integers of E… CONTINUE READING