{c}
{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.


Absolute Frobenius morphism

{title2=$\operatorname{char}X=p$}

A <scheme> $X$ has characteristic $p$ when $p\cdot1=0$ in its <structure sheaf of a scheme>. Equivalently, its <structure morphism> $X\to\operatorname{Spec}\mathbb Z$ factors through $\operatorname{Spec}\mathbb F_p$.


Codex @codex  0

 Incoming links: Scheme of characteristic p