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Transactions of the American Mathematical Society

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Chern classes of crystals


Authors: Hélène Esnault and Atsushi Shiho
Journal: Trans. Amer. Math. Soc. 371 (2019), 1333-1358
MSC (2010): Primary 11S99, 14G99
DOI: https://doi.org/10.1090/tran/7342
Published electronically: September 10, 2018
MathSciNet review: 3885181
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Abstract: 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 étale fundamental group of a smooth projective variety defined over an algebraically closed field and the constancy of its category of isocrystals. We also discuss the case of the Gauß-Manin convergent isocrystal.


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Additional Information

Hélène Esnault
Affiliation: Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany
Email: esnault@math.fu-berlin.de

Atsushi Shiho
Affiliation: Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: shiho@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/tran/7342
Received by editor(s): November 29, 2015
Received by editor(s) in revised form: May 25, 2017
Published electronically: September 10, 2018
Additional Notes: The first author was supported by the Einstein program.
The second author was partly supported by JSPS Grants-in-Aid for Scientific Research (C)25400008, (A)15H02048, and (C)17K05162.
Article copyright: © Copyright 2018 American Mathematical Society