This question is motivated purely by curiosity. In algebraic geometry there is a major distinction between the world of characteristic $0$ and that of characteristic $p > 0$ with different methods, different results available etc. 


From reading a number of books and papers I got the idea that in the case of rigid analytic geometry the distinction between the two worlds is not that important. So my question is:


Are there results in rigid geometry that are only known to be true in characteristic $0$ (like Hironaka desingularisation in algebraic geometry), or vice-versa, results that are only known to be true in positive characteristic?



Rigid analytic geometry in characterstic 0 vs positive characteristic
Resolution of singularities for rigid analytic varieties of equal characteristic zero follows from resolution of singularities for schemes of characteristic zero (Nicaise, A trace formula for rigid analytic varieties etc., 2009, Proposition 2.43).


There are more examples where the characteristic plays a role, e.g. in Van der Put, Cohomology on affinoid spaces, 1982. Here the reason is the radius of convergence of the logarithm.


