Rigid τ-crystals
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1059-1082.

Nous présentons un analogue en égale charactéristique des F-isocristaux sur un anneau parfait, que nous appelons τ-crystaux rigides. Nous introduisons des polygones de Newton pour les τ-crystaux rigides, et nous montrons que ceux-ci peuvent être étudiés au moyen des τ-crystaux formels, qui sont analogues aux F-crystaux. Ainsi, nous démontrons un analogue du théorème de Grothendieck–Katz pour les τ-crystaux rigides qui proviennent d’un modèle formel.

We present an equicharacteristic analogue of F-isocrystals over perfect rings, which we call rigid τ-crystals. We introduce Newton polygons for rigid τ-crystals and show how these can be studied via formal τ-crystals, the natural analogue of F-crystals. This leads to an analogue of the Grothendieck–Katz theorem for rigid τ-crystals that admit a formal model.

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DOI : https://doi.org/10.5802/jtnb.1012
Classification : 14F30,  14G22
Mots clés : F-crystals, equicharacteristic, Grothendieck–Katz theorem, rigid geometry
@article{JTNB_2017__29_3_1059_0,
     author = {Ben Heuer},
     title = {Rigid $\tau $-crystals},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {1059--1082},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {3},
     year = {2017},
     doi = {10.5802/jtnb.1012},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1012/}
}
Ben Heuer. Rigid $\tau $-crystals. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1059-1082. doi : 10.5802/jtnb.1012. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1012/

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