In a recent [answer](http://mathoverflow.net/questions/44005/intuition-for-rational-functions/44040#44040) to a recent [question](http://mathoverflow.net/questions/44005/intuition-for-rational-functions), [BCnrd](http://mathoverflow.net/users/3927/bcnrd) wrote

> [...] beyond the coherent case one cannot expect information about a fiber (e.g., vanishing, 6 generators, etc.) to "propogate" to information in a neighborhoood (which would be the spirit behind the choice of word "coherent", I suppose). [...]

Is that what motivates the adjective *coherent*? Is this documented somewhere?