Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.
Integral and adelic aspect s of the Mumford-Tate conjecture
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Unpolarized Shafarevich conjectures for hyper-K\"ahler varieties
Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.