This semester I am attending a reading seminar on non-archimedean analytic geometry (a subject I know nothing about), roughly following the [notes of Conrad](http://math.arizona.edu/~swc/aws/07/speakers/index.html). 


Reading Conrad's notes (and e.g. those of Bosch) it struck me that the prime spectrum of affinoid algebras never seems to appear, only the maximal spectrum. Can somebody explain the reason for this? 



Why is the prime spectrum not useful in non-archimedean analytic geometry?
I am surprised that Brian got to this one first without making what I thought was another obvious comment: affinoids are Jacobson rings! A function which is zero at all points of an affinoid rigid space corresponds to an element of your affinoid algebra which is in all maximal ideals and hence (by Jacobson-ness) is nilpotent. For a general ring this certainly isn't true: the intersection of all prime ideals is the nilpotent elements, but the intersection of all maximal ideals might be bigger (think of a 1-dimensional local ring, for example). 


