G-Valued Galois Deformation Rings when $\ell \ne p$

Abstract

For a smooth group scheme $G$ over an extension of ${\mathbf{Z}}_p$ such that the generic fiber of $G$ is reductive, we study the generic fiber of the Galois deformation ring for a $G$-valued mod $p$ representation of the absolute Galois group of a finite extension of ${\mathbf{Q}}_{\ell }$ with $\ell \ne p$. In particular, we show it admits a regular dense open locus, and that it is equidimensional of dimension $\dim G$.

Cited by in corpus (2)

• Coherent Springer theory and the categorical Deligne-Langlands correspondence
• From $p$-modular to $p$-adic Langlands correspondences for $U(1,1)({\mathbb{Q}}_{p^2}/{\mathbb{Q}}_p)$: deformations in the non-supercuspidal case