Random pro-p groups, braid groups, and random tame Galois groups

TL;DR

This paper proposes a heuristic model for predicting the distribution of Galois groups of maximal pro-p extensions of Q unramified outside random primes, supported by theoretical and experimental evidence.

Contribution

It introduces a novel heuristic prediction framework for Galois group distributions inspired by Cohen-Lenstra heuristics, with supporting evidence.

Findings

Heuristic predicts Galois group distributions for random prime sets.

Theoretical evidence supports the heuristic's plausibility.

Experimental data aligns with the proposed predictions.

Abstract

We introduce a heuristic prediction for the distribution of the isomorphism class of the Galois group of the maximal pro-p extension of Q 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.