$\def\Aut{\mathrm{Aut}}$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?
$\mathrm{Aut}(\mathbb P)$ is isomorphic to $\mathrm{ Aut} (k(t) )$
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algebraic-geometry
projective-space
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8What's your definition of $\mathbb{P}^1$ and what's your definition of a morphism between projective varieties? – 2012-06-18