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In the case of local fields of positive characteristic we introduce an analogue of Fontaine's concept of Galois modules with crystalline height h ∈ N. If h = 1 these modules appear as geometric points of Faltings's strict modules. We obtain upper estimates for the largest upper ramification numbers of these modules and prove (under an additional assumption) that these estimates are sharp.doi:10.4310/pamq.2009.v5.n1.a14 fatcat:3tak3ps6fbhtfk5dmonio3lejy