Uniform bounds of base change conductors and link with the generalized Szpiro conjecture

Abstract

The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change conductor in terms of the dimension of $A$ and the degree of $k$. This allows us to reduce the generalized Szpiro conjecture to the semi-stable case.