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The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was proved by Y. She. For hyper-K\"ahler varieties, which are higher-dimensional analogs of K3 surfaces, Y. Andr\'e proved the Shafarevich conjecture for hyper-K\"ahler varieties of a given dimension and admitting a very ample polarization of bounded degree. InarXiv:2203.10391v1 fatcat:ty6z2foggnfcldg6u6jtgf5a5y