Perfect points on abelian varieties in positive characteristic

Damian Rössler

Let \(K\) be the function field over a smooth curve over a perfect field of characteristic \(p>0\). Let \(K_{\text{perf}}\) be the maximal purely inseparable extension of \(K\). Let \(A\) be an abelian variety over \(K\). We shall discuss the properties of the group \(A(K_{\text{perf}})\) 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.