Base change conductors through intersection theory and quotient singularities

TL;DR

This paper develops new methods to compute the base change conductor of Jacobians using intersection theory and quotient singularities, providing formulas for tame and wild parts, especially in cases of potential good reduction.

Contribution

It introduces a systematic approach for calculating the base change conductor, including explicit formulas and computations for wild parts via Galois quotients of semistable models.

Findings

Derived a general formula for the tame part of the base change conductor.

Computed the wild part in terms of Galois quotients of models.

Analyzed cases with potential good reduction and weak wild 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 semistable 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.