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Nov 24 at 4:56 comment added abx The weaker conjecture (finite-dimensionality) is not known, even over $\mathbb{C}$. You can look for instance at this paper, Remark 2.2, for a list of special K3 where it holds, but the general case is wide open.
Nov 24 at 0:09 history asked Vik78 CC BY-SA 4.0