  A conjecture, recently stated by Flach and Morin, relates the action of the
monodromy on the Galois invariant part of the p-adic Beilinson-Hyodo-Kato
cohomology of the generic fiber of a scheme defined over a DVR of mixed
characteristic to (the cohomology of) its special fiber. We prove the
conjecture in the case the special fiber, of the given arithmetic scheme, is
also a fiber of a geometric family over a curve in positive characteristic.
