Full faithfulness for overconvergent F-de Rham–Witt connections

Veronika Ertl

doi:10.1016/j.crma.2016.04.004

Number theory/Algebraic geometry

Full faithfulness for overconvergent F-de Rham–Witt connections

Presented by: the Editorial Board

Veronika Ertl ¹

¹ Universität Regensburg, Fakultät für Mathematik, Universitätsstraße 31, 93053 Regensburg, Germany

Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 653-658.

Abstract
Résumé

Let X be a smooth variety over a perfect field of characteristic $p > 0$ . We define overconvergent F-de Rham–Witt connections as an analogue for F-crystals over proper schemes. We prove that the forgetful functor from the category of overconvergent F-de Rham–Witt connections to the category of convergent F-de Rham–Witt connections is fully faithful.

Soit X une variété lisse sur un corps parfait de charactéristique $p > 0$ . On définit les F-connections de de Rham–Witt surconvergentes comme analogues de F-cristaux sur les schémas propre. On montre que le foncteur oubli de la catégorie de F-connections de de Rham–Witt surconvergentes à la catégorie de F-connections de de Rham–Witt convergentes est pleinement fidèle.

Received: 2015-11-16
Accepted: 2016-04-11
Published online: 2016-04-22

DOI: 10.1016/j.crma.2016.04.004

Author's affiliations:

Veronika Ertl ¹

¹ Universität Regensburg, Fakultät für Mathematik, Universitätsstraße 31, 93053 Regensburg, Germany

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Veronika Ertl. Full faithfulness for overconvergent F-de Rham–Witt connections. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 653-658. doi : 10.1016/j.crma.2016.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.004/

References
Cited by

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[6] V. Ertl Overconvergent Chern classes and higher cycle classes, 2013 | arXiv

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[9] K.S. Kedlaya Full faithfulness for overconvergent F-isocrystals (A. Adolphson; F. Baldassarri; P. Berthelot; N. Katz; F. Loeser, eds.), Geometric Aspects of Dwork Theory II, de Gruyter, Berlin, 2004, pp. 819-835

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