Variétés abéliennes CM et grosse monodromie finie sauvage

2021/03/06 by Philip, Séverin · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.04197

Abstract

In this paper we study the wild part of the finite monodromy groups of abelian varieties over number fields. We solve Grunwald problems for groups of the form Z/pZ\wr \mathfrakS_n over number fields to build CM abelian varieties with maximal wild finite monodromy in the odd prime case. For the even prime case we prove a new bound on the 2-part of the order of the finite monodromy group for CM abelian varieties and build varieties that reach it.

Cited by

• The local obstruction to semi-stable reduction for abelian varieties

Related

• Groupes de monodromie finie des variétés abéliennes
• Determining monodromy groups of abelian varieties
• Big monodromy theorem for abelian varieties over finitely generated fields
• Reductions of abelian varieties of generalized Mumford type
• Jumps and monodromy of abelian varieties