2022
DOI: 10.48550/arxiv.2203.10391
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Unpolarized Shafarevich conjectures for hyper-Kähler varieties

Abstract: 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-Kähler varieties, which are higher-dimensional analogues of K3 surfaces, Y. André proved the Shafarevich conjecture for hyper-Kähler varieties of a given dimension and admitting a very ample polarization of bounded degree. In this paper, we provid… Show more

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