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arXiv · 2502.15052

Explicit modularity of K3 surfaces with complex multiplication of large degree

Edgar Costa·Andreas-Stephan Elsenhans·Jörg Jahnel·John Voight
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Abstract

We consider the transcendental motive of three K3 surfaces $X$ conjectured to have complex multiplication (CM). Under this assumption, we match these to explicit algebraic Hecke quasi-characters $\psi_X$, and CM abelian threefolds $A$. This provides substantial evidence that a power of $A$ corresponds to $X$ under the Kuga-Satake correspondence.

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Edgar Costa, Andreas-Stephan Elsenhans, Jörg Jahnel, John Voight. 2025-02-20. Explicit modularity of K3 surfaces with complex multiplication of large degree. https://arxiv.org/abs/2502.15052

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