Base change conductors through intersection theory and quotient singularities

2024/10/20 by Eriksson, Dennis, Halle, Lars Halvard, Nicaise, Johannes
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.15370

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.

Related

• Chai's conjectures on base change conductors
• Néron models and base change
• Uniform bounds of base change conductors and link with the generalized Szpiro conjecture
• A refinement of the Artin conductor and the base change conductor
• Géométrie non-commutative, formule des traces et conducteur de Bloch