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

Abstract

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.

38 pages. This paper replaces the previous preprint "Models over a d.v.r. of unequal caracteristic" arXiv:0803.3702. To appear on Journal of Algebra