Fourier-Mukai partners of K3 surfaces in positive characteristic

@article{Lieblich2011FourierMukaiPO,
  title={Fourier-Mukai partners of K3 surfaces in positive characteristic},
  author={Max Lieblich and Martin C. Olsson},
  journal={arXiv: Algebraic Geometry},
  year={2011}
}
We study Fourier-Mukai equivalence of K3 surfaces in positive characteristic and show that the classical results over the complex numbers all generalize. The key result is a positive-characteristic version of the Torelli theorem that uses the derived category in place of the Hodge structure on singular cohomology; this is proven by algebraizing formal lifts of Fourier-Mukai kernels to characteristic zero. As a consequence, any Shioda-supersingular K3 surface is uniquely determined up to… Expand
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References

SHOWING 1-10 OF 38 REFERENCES
Twisted sheaves and the period-index problem
  • 108
  • PDF
Néron–Severi groups under specialization
  • 47
  • PDF
Derived and abelian equivalence of K3 surfaces
  • 51
  • PDF
Moduli of twisted sheaves
  • 118
  • PDF
Fourier-Mukai transforms in algebraic geometry
  • 630
  • PDF
Semistable sheaves in positive characteristic
  • 263
  • Highly Influential
  • PDF
...
1
2
3
4
...