Chern classes of crystals

Research paper by Hélène Esnault, Atsushi Shiho

Indexed on: 21 Nov '15Published on: 21 Nov '15Published in: Mathematics - 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.