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

2012/11/02 by H. Lu, Huajun Lu, Lu, Huajun
Mathematics · #11G10 #11G50 #14G40 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:11G10 #msc:11G50 #msc:14G40

paper · pdf · doi:10.48550/arxiv.1211.0451

This paper has been withdrawn by the author due to a crucial error in the main theorem

openalex publication_date 2012/11/02 · arxiv created 2014/03/11 · arxiv updated 2014/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Related

• Chai's conjectures on base change conductors
• Heights, ranks and regulators of abelian varieties
• Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields
• Base change conductors through intersection theory and quotient singularities
• Smallness of Faltings heights of CM abelian varieties