The Masser-Wustholz theorem gives a bound for the degree of an isogeny between abelian varieties over number fields. However it tells us nothing about how the isogeny is related to polarisations of the abelian varieties. Compatibility between polarisations and isogenies is important for some applications such as the André-Pink conjecture on unlikely intersections. In this talk I will discuss bounds for the degree of isogenies which respect the polarisations.
