The de Jong fundamental group of a non-trivial abelian variety is non-abelian

Paper

Abstract

We show the de Jong fundamental group of any non-trivial abelian variety over a complete algebraically closed extension

is non-abelian. Generalizing an argument for

, we also show the de Jong fundamental groups of positive-dimensional quasi-projective rigid analytic varieties over

(including abelian varieties) depend on

and can be arbitrarily large.