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• W3037944244 abstract "Let k be a number field. We give an explicit bound, depending only on [k:ℚ] and the discriminant of the Néron–Severi lattice, on the size of the Brauer group of a K3 surface X/k that is geometrically isomorphic to the Kummer surface attached to a product of isogenous CM elliptic curves. As an application, we show that the Brauer–Manin set for such a variety is effectively computable. Conditional on GRH, we can also make the explicit bound depend only on [k:ℚ] and remove the condition that the elliptic curves be isogenous. In addition, we show how to obtain a bound, depending only on [k:ℚ], on the number of C-isomorphism classes of singular K3 surfaces defined over k, thus proving an effective version of the strong Shafarevich conjecture for singular K3 surfaces." @default.
• W3037944244 created "2020-07-02" @default.
• W3037944244 creator A5041812155 @default.
• W3037944244 creator A5051550520 @default.
• W3037944244 creator A5056029659 @default.
• W3037944244 date "2023-05-12" @default.
• W3037944244 modified "2023-10-14" @default.
• W3037944244 title "Explicit uniform bounds for Brauer groups of singular K3 surfaces" @default.
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• W3037944244 doi "https://doi.org/10.5802/aif.3526" @default.
• W3037944244 hasPublicationYear "2023" @default.
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