The Shafarevich conjecture for K3 surfaces
-- Yiwei She, November 7, 2014

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Let K be a number field, S a finite set of places of K, and g a
positive integer.  Shafarevich made the following conjecture
for higher genus curves: the set of isomorphism classes of
genus g curves defined over K and with good reduction outside
of S is finite.  In 1983, Faltings proved this conjecture for
curves and the analogous conjecture for polarized abelian
surfaces.  Building on the work of Faltings and Andre, we
prove the stronger unpolarized Shafarevich conjecture for K3
surfaces.