Mathematical Research Letters

Volume 26 (2019)

Number 4

$G$-valued Galois deformation rings when $\ell \neq p$

Pages: 973 – 990



Jeremy Booher (School of Mathematics and Statistics, University of Canterbury, Christchurch New Zealand)

Stefan Patrikis (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)


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 $\mathrm{mod} \: p$ representation of the absolute Galois group of a finite extension of $\mathbf{Q}_{\ell}$ with $\ell \neq p$. In particular, we show it admits a regular dense open locus, and that it is equidimensional of dimension $\mathrm{dim} \: G$.

Received 8 November 2017

Accepted 26 June 2018

Published 25 October 2019