Mathematics – Number Theory
Scientific paper
2007-07-11
Mathematics
Number Theory
48 pages. Preprint from MPI, Bonn. The paper is only the third splitting of http://www.arxiv.org/abs/math/0311042 The other tw
Scientific paper
We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0,p). As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type. As a second application, for p>2 (resp. for p=2) we prove the existence in unramified mixed characteristic (0,p) of integral canonical models of Shimura varieties of Hodge type that have compact factors (resp. that have compact factors and that pertain to abelian varieties in characteristic p which have zero p-ranks). Though the second application is new only for p<5 and for non-unitary Shimura varieties, its proof is new, more direct, and more of a principle. The second application also represents progress toward the proof of a conjecture of Milne.
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