3 problems

Let $Z$ be a smooth irreducible variety over $k$, and let $\varphi:Z\to I(x)$ be a nontrivial map, where $I(x)$ is an isogeny leaf. Non-liftability conjecture for maps into isogeny…

Let $\mathcal{X}/C$ be an abelian scheme and suppose it does not admit an isotrivial abelian subscheme. If … then for some finite étale cover $C'\twoheadrightarrow C$, the…

Let $f:\mathcal{X}\to C$ be an abelian scheme, and suppose that the Hodge bundle $f_*\Omega^1_{\mathcal{X}/C}$ is non-nef. An isogeny-leaf factor conjecture predicts that this non-…