Abstract
We present a method to construct examples of K3 surfaces of geometric Picard rank 1. Our approach is a refinement of that of R. van Luijk. It is based on an analysis of the Galois module structure on étale cohomology. This allows us to abandon the original limitation to cases of Picard rank 2 after reduction modulo p. Furthermore, the use of Galois data enables us to construct examples that require significantly less computation time. © Copyright © Cambridge Philosophical Society 2011.
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CITATION STYLE
Elsenhans, A. S., & Jahnel, J. (2011). On the computation of the Picard group for K3 surfaces. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 151, pp. 263–270). https://doi.org/10.1017/S0305004111000326
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