Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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REPRESENTATIONS OF THE AUTOMORPHISM GROUP OF A SUPERSINGULAR K3 SURFACE OF ARTIN-INVARIANT 1 OVER ODD CHARACTERISTIC

  • Received : 2014.03.03
  • Accepted : 2014.04.23
  • Published : 2014.05.15
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Abstract

In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

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References

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  2. Non-liftability of automorphism groups of a K3 surface in positive characteristic vol.363, pp.3-4, 2015, https://doi.org/10.1007/s00208-015-1197-9
  3. A Lifting of an Automorphism of a K3 Surface over Odd Characteristic 2017, https://doi.org/10.1093/imrn/rnw071
  4. The representations of the automorphism groups and the Frobenius invariants of K3 surfaces vol.65, pp.1, 2014, https://doi.org/10.1307/mmj/1457101815