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arXiv · 1703.08868

Witt differentials in the h-topology

Veronika Ertl·Lance Edward Miller
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Abstract

Recent important and powerful frameworks for the study of differential forms by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodsky's h-topology have greatly simplified and unified many approaches. This article builds towards the goal of putting Illusie's de Rham-Witt complex in the same framework by exploring the h-sheafification of the rational de Rham-Witt differentials. Assuming resolution of singularities in positive characteristic one recovers a complete cohomological h-descent for all terms of the complex. We also provide unconditional h-descent for the global sections and draw the expected conclusions. The approach is to realize that a certain right Kan extension introduced by Huber-Kebekus-Kelly takes the sheaf of rational de Rham-Witt forms to a qfh-sheaf. As such, we state and prove many results about qfh-sheaves which are of independent interest.

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BibTeXRIS

Veronika Ertl, Lance Edward Miller. 2017-03-26. Witt differentials in the h-topology. https://doi.org/10.1016/j.jpaa.2019.03.022

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