Number Theory Seminar

Speaker: Severin Philip (Stockholm University)

Title: Semi-stable reduction of abelian varieties and (p,t,a)-inertial groups

Abstract: I will first present the question of the semi-stability degree of abelian varieties in fixed dimension with an optimal solution which leads to an effective version of Grothendieck's semi-stable reduction. I will then introduce the central objects in this work : the finite monodromy groups,  with their properties and a first characterization of those. The rest of the talk will be dedicated to the question of Silverberg and Zarhin and their notion of (p,t,a)-inertial groups which is a conjectural characterization of the finite monodromy groups in dimension g=t+a. We will see that in most cases, (p,t,a)-inertial groups are indeed realizable as finite monodromy groups of abelian varieties of the correct dimension.