The weight part of Serre's conjecture over CM fields

TL;DR

This paper proves the weight part of Serre's conjecture for mod p Galois representations over certain CM fields, under specific technical and ramification assumptions.

Contribution

It establishes the weight part of Serre's conjecture for CM fields with tame ramification and generic conditions at p, extending previous results.

Findings

Proved the weight part of Serre's conjecture in the specified setting.

Identified conditions under which the conjecture holds for CM fields.

Extended the scope of Serre's conjecture to new classes of fields.

Abstract

Under some technical assumptions of a global nature, we establish the weight part of Serre's conjecture for mod $p$ Galois representations for CM fields that are tamely ramified and sufficiently generic at $p$.