  Recently, in order to formulate a categorical version of the local Langlands
correspondence, several authors have constructed moduli spaces of
$\mathbf{Z}[1/p]$-valued L-parameters for $p$-adic groups. The connected
components of these spaces over various $\mathbf{Z}[1/p]$-algebras $R$ are
conjecturally related to blocks in categories of $R$-representations of
$p$-adic groups. Dat-Helm-Kurinczuk-Moss described the components when $R$ is
an algebraically closed field and gave a conjectural description when $R =
\overline{\mathbf{Z}}[1/p]$. In this paper, we prove a strong form of this
conjecture applicable to any integral domain $R$ over
$\overline{\mathbf{Z}}[1/p]$.
