Frobenius map

Let $K$ be any field of characteristic $p>0$ , and suppose $K$ contains the finite field $\\mathbb{F}_{q}$ of size $q$ , where $q=p^{r}$ . The $q^{\\rm th}$ power Frobenius map on $K$ is the map $\\operatorname{Frob}_{q}:K\\longrightarrow K$ defined by $\\operatorname{Frob}_{q}(x):=x^{q}$ .

If $K$ is perfect, then $\\operatorname{Frob}_{q}$ is an automorphism of $K$ which fixes $\\mathbb{F}_{q}$ , and accordingly is a member of the Galois group $\\operatorname{Gal}(K/\\mathbb{F}_{q})$ .

单词	FrobeniusMap
释义	Frobenius map Let $K$ be any field of characteristic $p>0$ , and suppose $K$ contains the finite field $\\mathbb{F}_{q}$ of size $q$ , where $q=p^{r}$ . The $q^{\\rm th}$ power Frobenius map on $K$ is the map $\\operatorname{Frob}_{q}:K\\longrightarrow K$ defined by $\\operatorname{Frob}_{q}(x):=x^{q}$ . If $K$ is perfect, then $\\operatorname{Frob}_{q}$ is an automorphism of $K$ which fixes $\\mathbb{F}_{q}$ , and accordingly is a member of the Galois group $\\operatorname{Gal}(K/\\mathbb{F}_{q})$ .
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