Cohen-Lenstra heuristics and bilinear pairings in the presence of roots of unity

Michael Lipnowski, Will Sawin, Jacob Tsimerman

Let $L/K$ be a quadratic extension of global fields. We study Cohen-Lenstra heuristics for the $\ell$-part of the relative class group $G_{L/K}:=\text{Cl}(L/K)$ when $K$ contai…