On the degree of semi-stable reduction

2021/07/28 by Philip, Séverin
#11G10 #14G25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.13613

Abstract

For an abelian variety A over a number field we study bounds depending only on the dimension of A for the minimal degree d(A) of a field extension over which A acquires semi-stable reduction. We first compute d(A) in terms of the cardinalities of the finite monodromy groups of A which leads to a bound on d(A) in terms of the classical Minkowski bound. We then show this bound is tight up to its 2-part by considering p-adic coverings of the local points of a universal abelian scheme.

Related

• Semistable reduction of abelian varieties over extensions of small degree
• Groupes de monodromie finie des variétés abéliennes
• Reductions of abelian varieties of generalized Mumford type
• The local obstruction to semi-stable reduction for abelian varieties
• The splitting of reductions of an abelian variety