Chern classes of crystals

  title={Chern classes of crystals},
  author={H'elene Esnault and Atsushi Shiho},
  journal={arXiv: Algebraic Geometry},
  • H'elene Esnault, Atsushi Shiho
  • Published 2015
  • Mathematics
  • arXiv: Algebraic Geometry
  • The crystalline Chern classes of the value of a locally free crystal vanish on a smooth variety defined over a perfect field. Out of this we conclude new cases of de Jong's conjecture relating the geometric \'etale fundamental group of a smooth projective variety defined over a perfect field and the triviality of its category of isocrystals. We also discuss the case of the Gau{\ss}-Manin convergent isocrystal. 
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