Models of μ_{p^2} over a discrete valuation ring of unequal characteristic

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 μp2, 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 Appendix A X. Caruso shows how to classify models of μp2, K, in the case of unequal characteristic, using the Breuil-Kisin theory. © 2010 Elsevier Inc. All rights reserved.