Sections over Finite Fields

Abstract

Let ${\mathbb{F}}_{q}$ be a finite field with q elements of characteristic p. The absolute Galois group ${\mathrm{Gal}}_{{\mathbb{F}}_{q}}$ is profinite free and generated by the qth-power Frobenius ${Frob }_{q}$. Thus any extension of ${\mathrm{Gal}}_{{\mathbb{F}}_{q}}$ splits, and does so most likely in an abundant number of inequivalent ways.