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May 15, 2013 at 13:40 vote accept Cyrille Corpet
May 15, 2013 at 13:12 comment added naf No. Let $f:A \to B$ be a separable isogeny and $D$ a smooth ample divisor in $B$. Then $f^{−1}(D)$ is irreducible if $\dim(X)>1$ (since it is smooth and connected) and is stabilized by the kernel of $f$.
May 15, 2013 at 13:11 answer added Felipe Voloch timeline score: 2
May 15, 2013 at 12:44 history asked Cyrille Corpet CC BY-SA 3.0