2010/04/03 by Kedlaya, Kiran S.
#13F35 #14G22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1004.0466
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 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).