= Frobenius endomorphism of an algebraic group
{c}
{title2=$F:G\to G$}
= Frobenius endomorphisms of an algebraic group
{c}
{synonym}
For an <algebraic group> defined over $\mathbb F_q$, its Frobenius morphism acts as entrywise $q$th powers in a standard matrix realization. Its differential is zero, and its fixed-point group is finite. A conjugate $F'=\varphi F\varphi^{-1}$ defines an isomorphic rational structure. This group morphism must be distinguished from a field <Frobenius endomorphism> alone and from the convention called geometric Frobenius in Galois theory, which is inverse to the arithmetic generator on field points.
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