Séverin Philip

Semi-stable reduction of abelian varieties

Let A be an abelian variety over a number field K. The famous 'semi-stable reduction' theorem of Grothendieck gives us a finite extension L/K such that A_L has semi-stable reduction. This allows us to define the minimal degree of an extension on which A has semi-stable reduction, an integer depending only on A. We can go further and define the lowest common multiple of all such integers over all abelian varieties of fixed dimension over a (varying) number field. The goal of the talk is to give some results on the computation of these values. In that end, I will recall the different notions at play working from the case of elliptic curves.