On the \(1\)-cohomology of finite groups of Lie type (Q1355541)

Let \(G\) be a simply connected algebraic group defined and split over \(\mathbb{F}_p\) and let \(G(n)\) denote the rational points over \(\mathbb{F}_{p^n}\). The main result of this paper is to determine a uniform bound, \(N(G,p)\), such that for all \(n>N(G,p)\) and all \(p^n\) restricted highest weights, \(\lambda\), restriction gives an isomorphism \(H^1(G,L(\lambda))\leftrightarrow H^1(G(n),L(\lambda))\). Explicit formulae for \(N(G,p)\) are given in terms of weights.