Abstract:

This is joint work with Yifan Wei and John Yin. Recently, Cremona, Bhargava, Fisher and Gajovic conjectured that certain naturally occurring factorization densities over the p-adics should form a rational function in the prime p and have a functional equation. Inspired by this conjecture, we develop a framework for a p-adic analogue of the Chebotarev density theorem and prove it assuming the existence of nice resolutions. As a consequence of this general framework, we prove the above conjecture on factorization densities completely by constructing a nice resolution of the "resultant locus".