• Corpus ID: 104292609

Perfect points on genus one curves and consequences for supersingular K3 surfaces

  title={Perfect points on genus one curves and consequences for supersingular K3 surfaces},
  author={Daniel Bragg and Max Lieblich},
  journal={arXiv: Algebraic Geometry},
We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus one curves over function fields admit no points over the perfect closure of the base field) and use it to show that any non-Jacobian elliptic structure on a very general supersingular K3 surface has no purely inseparable multisections. We also describe specific examples of such fibrations without purely inseparable multisections. Finally, we discuss the… 

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