Correspondences on Shimura curves and Mazur’s principle at p

Abstract

In this paper, we continue our earlier study of Mazur’s Principle for totally real fields, and extend the main result to one also applicable to primes dividing the characteristic. The method we use is a naive generalisation of that of Mazur and Ribet. 1. Introduction. Let F be a totally real field of degree d over Q, and let ℓ be an odd prime. We recall the main result of [12], as improved by Fujiwara’s unpublished work[10]: Theorem 1.1 (Mazur’s Principle). Assume that