Shimura subgroups and degeneracy maps

Abstract

For M ≥ 1 an integer and M′ a positive divisor of M, let φ: J0(M′)τ → J0(M) be the map defined by all the degeneracy maps, where τ is the number of positive divisors of M/M′. We determine the kernel of φ for certain M and M′, as well as relate the pre-image of the Shimura subgroup Σ(M) under φ to the group Σ(M′)τ. We also study the restriction of degeneracy maps to Shimura subgroups.