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

TL;DR

This paper extends previous results on the rational cohomology of discriminant complements to algebraically closed fields of finite characteristic, providing explicit divisibility conditions related to automorphism groups of hypersurfaces.

Contribution

It generalizes earlier work to finite characteristic fields and offers explicit formulas for automorphism group orders in this setting.

Findings

Explicit divisibility formulas for automorphism group orders

Extension of cohomology results to finite characteristic fields

Connections between cohomology and automorphism groups in algebraic geometry

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 $p$.