Published November 2019
| Submitted
Journal Article
Open
On higher direct images of convergent isocrystals
- Creators
- Xu, Daxin
Abstract
Let k be a perfect field of characteristic p>0 and let W be the ring of Witt vectors of k. In this article, we give a new proof of the Frobenius descent for convergent isocrystals on a variety over k relative to W. This proof allows us to deduce an analogue of the de Rham complexes comparison theorem of Berthelot [D-modules arithmétiques. II. Descente par Frobenius, Mém. Soc. Math. Fr. (N.S.) 81 (2000)] without assuming a lifting of the Frobenius morphism. As an application, we prove a version of Berthelot's conjecture on the preservation of convergent isocrystals under the higher direct image by a smooth proper morphism of k-varieties.
Additional Information
© 2019 Foundation Compositio Mathematica. Received 15 March 2018, accepted in final form 3 June 2019. Published online by Cambridge University Press: 25 September 2019. I would like to thank Ahmed Abbes for discussions and his comments on an earlier version of this paper. I would like to thank Atsushi Shiho for his comments and suggestions for improving Theorem 1.9. I would like to thank Arthur Ogus for helpful discussions. I am also grateful to anonymous referees for their careful reading and valuable comments. Part of the work was done when the author was at the Beijing International Center for Mathematical Research (BICMR) and Institut des Hautes Études Scientifiques (IHÉS), and the author would like to thank them for their hospitality.Attached Files
Submitted - 1802.09060.pdf
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Additional details
- Eprint ID
- 99212
- DOI
- 10.1112/S0010437X19007590
- Resolver ID
- CaltechAUTHORS:20191010-112152558
- Created
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2019-10-10Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field