Projective integral models of Shimura varieties of Hodge type with compact factors
by
Adrian Vasiu
University of Arizona

Let (G, X) be a Shimura pair of Hodge type. We assume that each simple factor of the adjoint group of G, has simple, compact factors over the reals. Then we show that suitable quotients of finite type of the Shimura variety Sh(G, X), have natural projective integral models over Z[¹/_N] (here N > 2 is arbitrary). This result: (i) can be interpreted as a substantial progress in the proof of a conjecture of Morita, and (ii) provides in arbitrary mixed characteristic the very first examples of general nature of projective varieties over number fields which are not embeddable into abelian varieties and which have Néron models over certain localizations of rings of integers of number fields

Paper reference: arXiv:math.NT/0408421

Date received: March 28, 2005