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From: "Prof. Peter Johnstone"
Newsgroups: gmane.science.mathematics.categories
Subject: Re: equivalent varieties
Date: Mon, 28 Apr 2003 11:50:59 +0100 (BST)
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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