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arXiv · 1802.09060

On higher direct images of convergent isocrystals

Daxin Xu
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Abstract

Let k be a perfect field of characteristic p>0 and W 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 comparaison theorem of Berthelot 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.

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Daxin Xu. 2018-02-25. On higher direct images of convergent isocrystals. https://doi.org/10.1112/s0010437x19007590

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