We introduce a heuristic prediction for the distribution of the isomorphism class of the Galois group of the maximal pro- extension of unramified outside a “random” set of primes. This is guided by reasoning similar to that governing the Cohen–Lenstra conjectures. We conclude by describing theoretical and experimental evidence for our heuristic.
Cite this article
Nigel Boston, Jordan S. Ellenberg, Random pro- groups, braid groups, and random tame Galois groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 265–280DOI 10.4171/GGD/127