The unpolarized Shafarevich Conjecture for K3 Surfaces
classification
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surfacesconjecturefinitefixedshafarevichunpolarizedandraway
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We prove the unpolarized Shafarevich conjecture for K3 surfaces: the set of isomorphism classes of K3 surfaces over a fixed number field with good reduction away from a fixed and finite set of places is finite. Our proof is based on the theorems of Faltings and Andr\'e, as well as the Kuga-Satake construction.
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Forward citations
Cited by 2 Pith papers
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Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
Finiteness of isomorphism classes of generic fibers in pointed locally trivial families of Q-factorial terminal primitive symplectic varieties with fixed special fiber, plus projective finiteness under semi-ampleness,...
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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.
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