Let $M$ be an algebraic family of isocrystals over a base scheme $R/\mathbb{Q}_p$ (not a rigid analytic space).
The question is: is the set of weakly admissible points (i.e., the points $r\in R$ over which $M$ is weakly admissible) Zariski closed or open (or neither)?
The question seems to (in my case) come down to determining if the points $r\in R$ where $v_p(\mathrm{det} M_r)$ (where $M_r$ is the fiber above $r$) is bounded above, is Zariski closed/open/neither. Here $v_p$ is the $p$-adic valuation.
The answer might be very simple and/or well-known, but I haven't been able to figure it out.
Thanks for any help!
