Potentially semistable deformation rings for representations with values in $\mathrm{PGL}_n$
Volume 217 / 2025
Acta Arithmetica 217 (2025), 197-234
MSC: Primary 11F80; Secondary 11F85
DOI: 10.4064/aa230707-23-10
Published online: 31 January 2025
Abstract
We study the potentially semistable deformation rings for Galois representations taking their values in ${\rm PGL}_n$, by comparing them to the deformation rings for ${\rm GL}_n$. As an application, we state an analogue of the Breuil–Mézard conjecture, and we show that the case of ${\rm PGL}_n$ follows from the case of ${\rm GL}_n$.
