### Question
Say we have a map, C->D, of relative curves over a Dedekind scheme, S. What methods are available of showing that this map has good reduction, or integral reduction, at some s∈S? By this I mean: what are some popular conditions that imply this? What are the tricks people usually use?
### Clarification
By a map having good reduction I mean that both C<sub>s</sub> and D<sub>s</sub> are regular integral curves. By integral reduction I mean that both C<sub>s</sub> and D<sub>s</sub> are integral curves.
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You may assume whatever you want, this is part of the question. Assuming, for example, that C->D is generically Galois; or that D is smooth over S; is legitimate. This is pretty open-ended. Hence, community wiki.