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March 2013 Nonarchimedean geometry of Witt vectors
Kiran S. Kedlaya
Nagoya Math. J. 209: 111-165 (March 2013). DOI: 10.1215/00277630-1959469

Abstract

Let R be a perfect Fp-algebra equipped with the trivial norm. Let W(R) be the ring of p-typical Witt vectors over R equipped with the p-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate a close analogy between W(R) and the polynomial ring R[T] equipped with the Gauss norm, in which the role of the structure morphism from R to R[T] is played by the Teichmüller map. For instance, we show that the analytic space associated to R is a strong deformation retract of the space associated to W(R). We also show that each fiber forms a tree under the relation of pointwise comparison, and we classify the points of fibers in the manner of Berkovich’s classification of points of a nonarchimedean disk. Some results pertain to the study of p-adic representations of étale fundamental groups of nonarchimedean analytic spaces (i.e., relative p-adic Hodge theory).

Citation

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Kiran S. Kedlaya. "Nonarchimedean geometry of Witt vectors." Nagoya Math. J. 209 111 - 165, March 2013. https://doi.org/10.1215/00277630-1959469

Information

Published: March 2013
First available in Project Euclid: 27 February 2013

zbMATH: 1271.14029
MathSciNet: MR3032139
Digital Object Identifier: 10.1215/00277630-1959469

Subjects:
Primary: 14G22
Secondary: 13F35

Rights: Copyright © 2013 Editorial Board, Nagoya Mathematical Journal

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Vol.209 • March 2013
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