Models of muₚ₂,ₖ over a discrete valuation ring

الأصل · EN

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 the appendix X. Caruso shows how to classify models of μₚ₂,ₖ, in the case of unequal characteristic, using the Breuil-Kisin theory.