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Nonarchimedean geometry of Witt vectors

Published online by Cambridge University Press:  11 January 2016

Kiran S. Kedlaya
Kiran S. Kedlaya*
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, California 92093, USA, [email protected]
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Abstract

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Let R be a perfect 𝔽-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).

Keywords

14G2213F35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 209 , March 2013 , pp. 111 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

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