Mazur's principle for U(1,d)

TL;DR

This paper generalizes Mazur's principle from classical modular forms to higher-dimensional unitary groups, analyzing torsion cohomology and local monodromy in Shimura varieties of Kottwitz-Harris-Taylor type.

Contribution

It extends Mazur's principle to certain higher-dimensional unitary groups, linking torsion cohomology with local monodromy degeneracy in Shimura varieties.

Findings

Established conditions for lifting torsion classes to characteristic zero

Connected local monodromy degeneracy with cohomological properties

Generalized Mazur's principle to non quasi split inner forms

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.