Regulated extensions independence-of-ell conjecture for A-motives

Let $F$ be a finite extension of the fraction field of $A$, let $\mathfrak p$ be a finite place of $F$, and let $\underline M$ be an $A$-motive over $F_{\mathfrak p}$. For a maximal ideal $\ell$ of $A$ distinct from the maximal ideal below $\mathfrak p$, let $\operatorname{Ext}^{1,\mathrm{reg}}_{\mathrm{good}}(\mathbbm{1},\underline M)_\ell$ denote the regulated extensions having good reduction in the $\ell$-adic realization.

Regulated independence-of-$\ell$ conjecture. The inclusion

$$\operatorname{Ext}^{1,\mathrm{reg}}_{\mathcal O_{\mathfrak p}}(\mathbbm{1},\underline M)\subseteq\operatorname{Ext}^{1,\mathrm{reg}}_{\mathrm{good}}(\mathbbm{1},\underline M)_\ell$$

is an equality. In particular, $\operatorname{Ext}^{1,\mathrm{reg}}_{\mathrm{good}}(\mathbbm{1},\underline N)_\ell$ does not depend on $\ell$.

This is stated as a strong expectation after the inclusion supplied by the source's main theorem; it is a local regulated analogue of the equality between integral and good-reduction extensions.