Explicit uniform bounds for Brauer groups of singular K3 surfaces

Balestrieri, F., Johnson, A. and Newton, R. ORCID: https://orcid.org/0000-0003-4925-635X (2023) Explicit uniform bounds for Brauer groups of singular K3 surfaces. Annales de l'Institut Fourier, 73 (2). pp. 567-607. ISSN 0373-0956 doi: 10.5802/aif.3526

Abstract/Summary

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
URI	https://reading-clone.eprints-hosting.org/id/eprint/99898
Identification Number/DOI	10.5802/aif.3526
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Association des Annales de l'Institut Fourier
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