Convergent isocrystals on simply connected varieties
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, p. 2109-2148
It is conjectured by de Jong that, if X is a connected smooth projective variety over an algebraically closed field k of characteristic p>0 with trivial étale fundamental group, any isocrystal on X is constant. We prove this conjecture under certain additional assumptions.
de Jong a conjecturé que sur une variété lisse projective connexe sur un corps algébriquement clos de caractéristique p>0, de groupe fondamental étale trivial, tout isocristal est constant. Nous prouvons cette conjecture sous certaines hypothèses supplémentaires.
Received : 2016-04-12
Revised : 2017-10-19
Accepted : 2017-11-14
Published online : 2018-11-23
DOI : https://doi.org/10.5802/aif.3204
Classification:  14F10,  14D20
Keywords: isocrystals, simply connected varieties
@article{AIF_2018__68_5_2109_0,
     author = {Esnault, H\'el\`ene and Shiho, Atsushi},
     title = {Convergent isocrystals on simply connected varieties},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     pages = {2109-2148},
     doi = {10.5802/aif.3204},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_5_2109_0}
}
Esnault, Hélène; Shiho, Atsushi. Convergent isocrystals on simply connected varieties. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2109-2148. doi : 10.5802/aif.3204. https://aif.centre-mersenne.org/item/AIF_2018__68_5_2109_0/

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