Re: equivalent varieties

On Sat, 26 Apr 2003, Prof. Peter Johnstone wrote:

The equivalence of these varieties for all p is well known. It's best understood by seeing that they are all dual to the category of Stone spaces: given a Stone space, the ring of continuous Z_p-valued functions on it (where Z_p is given the discrete topology) is a ring satisfying p1=0 and x^p=x; conversely, given such a ring, its prime (=maximal) ideal spectrum is a Stone space.

Not having my copy of "Stone Spaces" to hand as I write this, I can't remember whether this fact was in the book. But it certainly should have been.

Yes, it is there -- Exercise V 2.6, page 186. Peter Johnstone