Models of mu_{p^2,K} over a discrete valuation ring

Let R be a discrete valuation ring with residue field of characteristic p>0. Let K be its fraction field. We prove that any finite and flat R-group scheme, isomorphic to μ_{p^2,K} on the generic fiber, is the kernel in a short exact sequence which generically coincides with the Kummer sequence. We will explicitly describe and classify such models. In the appendix X. Caruso shows how to classify models of μ_{p^2,K}, in the case of unequal characteristic, using the Breuil-Kisin theory.

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