Mazur's Principle for Totally Real Fields of Odd Degree

In this paper, we prove an analogue of the result known as Mazur's Principle concerning optimal levels of mod Galois representations. The paper is divided into two parts. We begin with the study (following Katz–Mazur) of the integral model for certain Shimura curves and the structure of the special fibre. It is this study which allows us to generalise, in the second part of this paper, Mazur's result to totally real fields of odd degree.