Appears in collection : 2019 - T2 - WS2 - Rational points on irrational varieties

Let K be the function field over a smooth curve over a perfect field of characteristic p 0. Let Kperf be the maximal purely inseparable extension of K. Let A be an abelian variety over K. We shall discuss the properties of the group A(Kperf) and some of its subgroups. Most of the results we shall present rely on a simple theory relating the Harder-Narasimhan filtration of the Lie algebra of a finite group scheme to its subgroups