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Mathematics > Number Theory

arXiv:1805.06269 (math)
[Submitted on 16 May 2018 (v1), last revised 12 Apr 2019 (this version, v3)]

Title:A new proof of a vanishing result due to Berthelot, Esnault, and Rülling

Authors:Veronika Ertl
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Abstract:The goal of this small note is to give a more concise proof of a result due to Berthelot, Esnault, and Rülling. For a regular, proper, and flat scheme $X$ over a discrete valuation ring of mixed characteristic $(0,p)$, it relates the vanishing of the cohomology of the structure sheaf of the generic fibre of $X$ with the vanishing of the Witt vector cohomology of its special fibre. We use as a critical ingredient results and constructions by Beilinson and Nekovář--Nizioł related to the $h$-topos over a $p$-adic field.
Comments: 9 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11G25, 14F20, 14F17
Cite as: arXiv:1805.06269 [math.NT]
  (or arXiv:1805.06269v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.06269
Journal reference: Journal of Number Theory, 2019
Related DOI: https://doi.org/10.1016/j.jnt.2019.03.022

Submission history

From: Veronika Ertl [view email]
[v1] Wed, 16 May 2018 12:25:46 UTC (12 KB)
[v2] Mon, 21 May 2018 14:52:03 UTC (12 KB)
[v3] Fri, 12 Apr 2019 07:53:19 UTC (13 KB)
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