The monodromy of F-isocrystals with log-decay

2016/12/04 by Kramer-Miller, Joe
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.01164

Abstract

Let U be a smooth geometrically connected affine curve over \mathbbF_p with compactification X. Following Dwork and Katz, a p-adic representation ρ of π₁(U) corresponds to an étale F-isocrystal. By work of Tsuzuki and Crew an F-isocrystal is overconvergent precisely when ρ has finite monodromy at each x ∈ X-U. However, in practice most F-isocrystals arising geometrically are not overconvergent and have logarithmic growth at singularities (e.g. characters of the Igusa tower over a modular curve). We give a Galois-theoretic interpretation of these log growth F-isocrystals in terms of asymptotic properties of higher ramification groups.

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