Rigid τ-crystals
Heuer, Ben1
1 The London School of Geometry and Number Theory Department of Mathematics University College London Gower Street, London WC1E 6BT, UK
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 : 10.5802/jtnb.1012
Classification : 14F30, 14G22
Mots-clés : $F$-crystals, equicharacteristic, Grothendieck–Katz theorem, rigid geometry
Heuer, Ben 1

1 The London School of Geometry and Number Theory Department of Mathematics University College London Gower Street, London WC1E 6BT, UK 
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Heuer, Ben. Rigid $\tau $-crystals. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 1059-1082. doi : 10.5802/jtnb.1012. http://www.numdam.org/articles/10.5802/jtnb.1012/

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