Re: equivalent varieties

["Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

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