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Explicit uniform bounds for Brauer groups of singular K3 surfaces

Balestrieri, F., Johnson, A. and Newton, R. ORCID: (2021) Explicit uniform bounds for Brauer groups of singular K3 surfaces. Annales de l'Institut Fourier. ISSN 0373-0956 (In Press)

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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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:99898
Publisher:Association des Annales de l'Institut Fourier

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