Potentially semi-stable deformation rings for representations with values in $PG{L}_n$

Abstract

We study the potentially semi-stable deformation rings for Galois representations taking their values in $PG{L}_n$, by comparing them to the deformation rings for $G{L}_n$. As an application, we state an analogue of the Breuil-Mézard conjecture, and we show that the case of $PG{L}_n$ follows from the case of $G{L}_n$.

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