Torsion points on modular curves

摘要

Let N ≥ 23 be a prime number. In this paper, we prove a conjecture of Coleman, Kaskel, and Ribet about the Q-valued points of the modular curve X_0(N) which map to torsion points on J_0(N) via the cuspidal embedding. We give some generalizations to other modular curves, and to noncuspidal embeddings of X_0(N) into J_0(N).