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$\def\Aut{\mathrm{Aut}}$I want to prove that the automorphism group of $\mathbb P^1$ it's isomorphic with the Moebius transformation with coefficients over the obvious field. I proved that the automorphism of $k(t)$ are of this form, If I prove that: $$\Aut(\mathbb P)\text{ is isomorphic to }\Aut (k(t) )$$ I'll be done. How can I do it, only using basic facts?

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    What's your definition of $\mathbb{P}^1$ and what's your definition of a morphism between projective varieties?2012-06-18

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