  We prove for abelian varieties a global form of Denef and Loeser's motivic
monodromy conjecture, in arbitrary characteristic. More precisely, we prove
that for every tamely ramified abelian variety $A$ over a complete discretely
valued field, its motivic zeta function has a unique pole at Chai's base change
conductor $c(A)$ of $A$, and that the order of this pole equals one plus the
potential toric rank of $A$. Moreover, we show that for every embedding of
$\Q_\ell$ in $\C$, the value $\exp(2\pi i c(A))$ is an $\ell$-adic tame
monodromy eigenvalue of $A$. The main tool in the paper is Edixhoven's
filtration on the special fiber of the N\'eron model of $A$, which measures the
behaviour of the N\'eron model under tame base change.
