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$\mathbb{A}_{\text{inf}}$ IS INFINITE DIMENSIONAL

Part of: Arithmetic rings and other special rings (Co)homology theory

Published online by Cambridge University Press:  11 May 2020

Jaclyn Lang  and
Judith Ludwig Open the ORCID record for Judith Ludwig [Opens in a new window]
Jaclyn Lang
Affiliation:
LAGA, UMR 7539, CNRS, Université Paris 13 - Sorbonne Paris Cité, Université Paris 8, France ([email protected])
Judith Ludwig
Affiliation:
IWR, University of Heidelberg, Im Neuenheimer Feld 205, 69120Heidelberg, Germany ([email protected])
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Abstract

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Given a perfect valuation ring $R$ of characteristic $p$ that is complete with respect to a rank-1 nondiscrete valuation, we show that the ring $\mathbb{A}_{\inf }$ of Witt vectors of $R$ has infinite Krull dimension.

Keywords

p-adic Hodge theoryFargues-Fontaine curvesKrull dimensionNewton polygons

MSC classification

Primary: 13F35: Witt vectors and related rings 13F25: Formal power series rings
Secondary: 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 6 , November 2021 , pp. 1983 - 1989
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020. Published by Cambridge University Press

References

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Kedlaya, Kiran, Some ring-theoretic properties of $\mathbb{A}_{\text{inf}}$ , preprint, 2018, arXiv:1602.09016v3.Google Scholar