2 problems

Let $X$ be an abelian variety and let $\sigma$ be an automorphism of $X$ that leaves invariant no proper subscheme. Let $\mathcal{L}$ be an ample invertible sheaf on $X$, and write…

Let $X$ be a projective $k$-scheme of any dimension, let $\sigma:X\to X$ be an automorphism, let $\mathcal{L}$ be a $\sigma$-ample invertible sheaf, and let…