Uniform bounds and effectivity results for singular K3 surfaces

Number Theory

26 April 16:40 - 17:10


This is joint work with Alexis Johnson and Rachel Newton. 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. 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.

Pär Kurlberg
KTH Royal Institute of Technology
Lilian Matthiesen
KTH Royal Institute of Technology
Damaris Schindler
Universität Göttingen


Pär Kurlberg

Lilian Matthiesen


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