Potentially semi-stable deformation rings for representations with values in PGL_n
Résumé
We study the potentially semi-stable deformation rings for Galois
representations taking their values in $\PGL_n$, by comparing them to the
deformation rings for $\GL_n$. As an application, we state an analogue of
the Breuil-Mézard conjecture, and we show that the case of $\PGL_n$
follows from the case of $\GL_n$.