Purity results for -divisible groups and Abelian schemes over regular bases of mixed characteristic
Adrian Vasiu
P. O. Box 6000, Department of Mathematical Sciences, Binghamton University, Binghamton, New York 13902-6000, USAThomas Zink
Fakultät für Mathematik, Universität Bielefeld, P.O. Box 100 131, 33 501 Bielefeld, Germany

Abstract
Let be a prime. Let be a regular local ring of mixed characteristic and absolute index of ramification . We provide general criteria of when each abelian scheme over extends to an abelian scheme over . We show that such extensions always exist if , exist in most cases if , and do not exist in general if . The case implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring of mixed characteristic and index of ramification at most . This leads to large classes of examples of Néron models over . If and index , the examples are new.
Cite this article
Adrian Vasiu, Thomas Zink, Purity results for -divisible groups and Abelian schemes over regular bases of mixed characteristic. Doc. Math. 15 (2010), pp. 571–599
DOI 10.4171/DM/307