I read this somewhere, I just want to confirm the authenticity.
If we have Galois covering $$X\longrightarrow P^{1}_{\mathbb{Q}}$$ defined over rationals which is cyclic. I mean the Galois Group associated to the covering is cyclic group. Then X can not be $P^{1}_\mathbb{Q}$
My first question is is this result true,
And if yes, Can we find some curve of higher genus where quotient is $P^{1}_\mathbb{Q}$