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• W3016442783 abstract "We show that there is no family of Enriques surfaces over the ring of integers. This extends non-existence results of Minkowski for families of finite étale schemes, of Tate and Ogg for families of elliptic curves, and of Fontaine and Abrashkin for families of abelian varieties and more general smooth proper schemes with certain restrictions on Hodge numbers. Our main idea is to study the local system of numerical classes of invertible sheaves. Among other things, our result also hinges on counting rational points, Lang's classification of rational elliptic surfaces in characteristic two, the theory of exceptional Enriques surfaces due to Ekedahl and Shepherd-Barron, some recent results on the base of their versal deformation, Shioda's theory of Mordell--Weil lattices, and an extensive combinatorial study for the pairwise interaction of genus-one fibrations." @default.
• W3016442783 created "2020-04-24" @default.
• W3016442783 creator A5082520908 @default.
• W3016442783 date "2023-01-01" @default.
• W3016442783 modified "2023-10-16" @default.
• W3016442783 title "There is no Enriques surface over the integers" @default.
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• W3016442783 doi "https://doi.org/10.4007/annals.2023.197.1.1" @default.
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