Séverin Philip: The obstruction to semi-stable reduction for abelian varieties

Abstract: In proving the semi-stable reduction theorem, Grothendieck gives a first description of the local obstruction. In this talk I will present a group theoretic characterization of this obstruction and show how it allows us to compute the semi-stability degree. I will first introduce the notion of semi-stable reduction starting from elliptic curves before discussing the semi-stability degree of abelian varieties. We will then see the notion of finite monodromy groups and their properties. Finally, I will give a characterization of these groups through the notion of (p,t,a)-inertial groups by Silverberg and Zarhin.