# Question about the Frobenius morphism [closed]

I read the proof of the Hasse Theorem at page 138 in "Arithmetic of elliptic curves" by J.Silverman and i don't understand why the Galois group of the extension $$\overline{\mathbb{F}}_q/\mathbb{F}_q$$ is generated by the $$q^{th}-$$power map on $$\overline{\mathbb{F}}_q$$.

• This is a basic question about Galois theory of finite fields, I fear this is not suitable for this forum. – Chris Wuthrich May 22 at 16:45
• @ChrisWuthrich $\overline{\mathbb{F}_p}$ is not a finite field – danihelovick May 23 at 22:18
• This isn't research-level, in part because it's incorrect - the Galois group of the algebraic closure of a finite field is the profinite completion of $\mathbb{Z}$. See math.stackexchange.com/a/586134/364828 – user44191 May 23 at 23:47
• @user44191 at page 138 it is said – danihelovick May 24 at 11:46
• Doesn't it say "(topologically) generated" ? – Chris Wuthrich May 24 at 12:59