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Let $X$ be a curve defined over a number field $K$, and let $G_K$ be the absolute Galois group of $K$. Let $\text{Aut}(X)$ be the group of $\overline{K}$-defined automorphisms of $X$, and consider the ...

1. Let $X$ be a smooth irreducible $\Bbb C$-variety, on which the algebraic $\Bbb C$-group $G={\bf G}_{a,{\Bbb C}}$ (the additive group) acts freely on the right: $$ X\times _{\Bbb C} G\to X,\quad (x,...