Absolute Frobenius morphism
= Absolute Frobenius morphism
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{title2=$F_X:X\to X$}
{wiki=Frobenius_morphism}
The absolute Frobenius morphism of a <scheme of characteristic p> is the identity on the underlying topological space and raises every local function to its $p$th power. On an affine chart $\operatorname{Spec}A$ it is induced contravariantly by the <Frobenius endomorphism> $A\to A$, $a\mapsto a^p$. It need not be an <isomorphism of schemes>, even when it acts invertibly on global sections.