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I was reading about elliptic curves from this PDF. Page 44 defines Frobenius map. It defines the frobenius map as $f(x,y) = (x^p, y^p) \bmod p$. Isn't it just an identity map? What's the use of this map in elliptic curves?

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  • $\begingroup$ For future reference: In SO, cross-posting on two different sites is not a good etiquette. Select one, and give the community a chance to answer. $\endgroup$ – kelalaka Dec 2 '18 at 11:11
  • $\begingroup$ Hint: $f$ is defined on $E(\overline{\mathbb F_p})$, the curve over the entire algebraic closure $\overline{\mathbb F_p}$ of $\mathbb F_p$. Under what circumstances is $x \mapsto x^p$ the identity on a field of characteristic $p$? migrated from answer, pursuant to [homework hinting policy] $\endgroup$ – Squeamish Ossifrage May 14 at 0:00

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