On behavior of conductors, Picard schemes, and Jacobian numbers of varieties over imperfect fields

Ippei Nagamachi, Teppei Takamatsu

Let $X$ be a regular geometrically integral variety over an imperfect field $K$. Unlike the case of characteristic $0$, $X^{\prime }:=X{\times }_{\mathrm{Spec}K}\mathrm{Spec}{K}^{\prime }$ may have s…