John Baez and James Dolan, 2023-10-02

The spectrum of a special commutative Frobenius algebra is a finite example of a Stone space, i.e. a compact Hausdorff space that is totally separated (which in the conversation we called 'totally disconnected'):
en.wikipedia.o...
Alternatively, a special commutative Frobenius algebra gives a scheme X where the diagonal D ⊆ X × X has a complement in the category of schemes.
Special commutative Frobenius algebras over ℤ are all completely trivial: just finite products of copies of ℤ. What about special commutative Frobenius algebras over A = ℤ[1/2, 1/3]? By Carboni's work the opposite of the category of these should be a boolean topos, roughly the topos of G-sets where G is some profinite group:
Aurelio Carboni, Matrices, relations, and group representations, www.sciencedir...
But here we study them more directly.
For more on this whole series of conversations, go here:
math.ucr.edu/h...