Does anybody happen to know if there is already a name in the literature for the following property of a mixed characteristic DVR: that there exists a local homomorphism that is regular into the specified DVR where the domain is a DVR whose residue field is a finite field?
Since the fraction field has characteristic $0$, the "regular" hypothesis is equivalent to asking that the image of the maximal ideal of the source DVR (the one with finite residue field) in the target DVR generates the maximal ideal of the target DVR.
