Base change conductors through intersection theory and quotient singularities

Abstract

We perform a systematic study of the base change conductor for Jacobians. Through the lens of intersection theory and Deligne’s Riemann–Roch theorem, we present novel computational approaches for both the tame and wild parts of the base change conductor. Our key results include a general formula of the tame part, as well as a computation of the wild part in terms of Galois quotients of semi-stable models of the curves. We treat in detail the case of potential good reduction when the quotient only has weak wild quotient singularities, relying on recent advances by Obus and Wewers.