Mathematics – Number Theory
Scientific paper
2010-04-03
Mathematics
Number Theory
44 pages; v5: refereed version; proofs of Theorem 5.11 and Theorem 6.8 corrected; additional minor corrections
Scientific paper
Let R be a perfect F_p-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 Teichmuller 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 fibre forms a tree under the relation of pointwise comparison, and classify the points of fibres in the manner of Berkovich's classification of points of a nonarchimedean disc. Some results pertain to the study of p-adic representations of etale fundamental groups of nonarchimedean analytic spaces (i.e., relative p-adic Hodge theory).
No associations
LandOfFree
Nonarchimedean geometry of Witt vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonarchimedean geometry of Witt vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonarchimedean geometry of Witt vectors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-448692