• DOI:10.1090/TRAN/7342
Corpus ID: 119614327

Chern classes of crystals

@article{Esnault2015ChernCO,
  title={Chern classes of crystals},
  author={H'elene Esnault and Atsushi Shiho},
  journal={arXiv: Algebraic Geometry},
  year={2015}
}

H'elene Esnault, Atsushi Shiho

Published 2015

Mathematics

arXiv: Algebraic Geometry

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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.