On weight elimination for $\mathrm{GL}_n (\mathbb{Q}_{p^f})$

We show that the modular Serre weights of a sufficiently generic $\mathrm{mod} \: p$ Galois representation of an unramified $p$-adic field are themselves generic, and give precise bounds on the genericity, by extending previous work of Emerton, Gee and Herzig. Our bounds are nearly optimal in some cases. We use this to improve recent weight elimination theorems.

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The author was supported by an NSERC grant while this work was carried out.

Received 16 February 2018

Accepted 12 July 2018

Published 7 June 2019