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Models of group schemes of roots of unity

A. MézardM. RomagnyD. Tossici — 2013

Annales de l’institut Fourier

Let 𝒪 K be a discrete valuation ring of mixed characteristics ( 0 , p ) , with residue field k . Using work of Sekiguchi and Suwa, we construct some finite flat 𝒪 K -models of the group scheme μ p n , K of p n -th roots of unity, which we call . We carefully set out the general framework and algebraic properties of this construction. When k is perfect and 𝒪 K is a complete totally ramified extension of the ring of Witt vectors W ( k ) , we provide a parallel study of the Breuil-Kisin modules of finite flat models of μ p n , K , in such a...

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