Mazur's principle for U(1,d)

Abstract

The Mazur principle give simple conditions for an irreducible unramified $\overline{{\mathbb{F}}_l}$-representation coming from a modular form of level ${\Gamma }_0(Np)$ to come for some modular form of level ${\Gamma }_0(N)$. The aim of this work is to give a generalization of this principle in higher dimension for some particular extended inner forms non quasi split of a unitary group studying the torsion cohomology classes of Shimura varieties of Kottwitz-Harris-Taylor type within its link with the local monodromy degeneracy.

arXiv commentin French. arXiv admin note: text overlap with arXiv:1503.03303