Three arithmetic sites

Abstract

Two new arithmetic sites are introduced, based on dynamical Belyi maps and Conway's big picture, respectively. We relate these to arboreal Galois representations, Bost-Connes data, and the original arithmetic site due to Connes and Consani.

Idempotents and the points of the topos of M-sets

“…In recent years, there was a considerable attention to the problem of understanding the points and possible topological space structures on E = S M . When M = N × + is the multiplicative monoid of strictly positive natural numbers there is an interesting topological space structure on the set F(S M ) studied by Connes-Consani [2] and Le Bruyn [10], see also a related paper by Hemelaer [6].…”