PUB - Publikationen an der Universität Bielefeld

Let p be a prime. Let (R, m) be a regular local ring of mixed characteristic (0, p) and absolute index of ramification e. We provide general criteria of when each abelian scheme over Spec R \ {m} extends to an abelian scheme over Spec R. We show that such extensions always exist if e <= p-1, exist in most cases if p <= e <= 2 p-3, and do not exist in general if e >= 2p-2. The case e >= p-1 implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring O of mixed characteristic (0, p) and index of ramification at most p - 1. This leads to large classes of examples of Neron models over O. If p > 2 and index p - 1, the examples are new.