Division theorems for the rational cohomology of discriminant complements and applications to automorphism groups in finite characteristic

Abstract

In this note we extend some of the results of a previous paper \url{arXiv:math/0511593} to algebraically closed fields of finite characteristic. In particular, we show that there is an explicit expression in $n$ and $d$ which is divisible by the prime to $p$ part of the order of the the automorphism group of a smooth degree $d$ hypersurface $\subset \mathbb{P}^n_k$ for $k$ an algebraically closed field of characteristic $p$.