# zbMATH — the first resource for mathematics

Integral models in unramified mixed characteristic $$(0,2)$$ of Hermitian orthogonal Shimura varieties of PEL type. II. (English) Zbl 1305.11056
The paper under review is a continuation of an earlier work [J. Ramanujan Math. Soc. 27, No. 4, 425–477 (2012; Zbl 1357.11062)] of the author. Its main goal is to prove the existence of integral canonical models of the so-called hermitian orthogonal Shimura varieties of PEL type in unramified mixed characteristic $$(0,2)$$. These PEL Shimura varieties are moduli spaces of polarized abelian schemes equipped with a suitable endomorphism algebra and level structure. The method in the paper is somehow standard – to prove the regularity and formal smoothness of the normalization of the schematic closure of a natural subscheme; however the technique is of high level.
Reviewer: Xin Lu (Mainz)

##### MSC:
 11G18 Arithmetic aspects of modular and Shimura varieties 14G35 Modular and Shimura varieties 11G10 Abelian varieties of dimension $$> 1$$ 11G15 Complex multiplication and moduli of abelian varieties 14F30 $$p$$-adic cohomology, crystalline cohomology 14K10 Algebraic moduli of abelian varieties, classification 14L05 Formal groups, $$p$$-divisible groups 11E57 Classical groups 20G25 Linear algebraic groups over local fields and their integers
Zbl 1357.11062
Full Text:
##### References:
 [1] Bosch, Néron models, Ergebnisse der Math. und ihrer Grenzgebiete (3) (1990) [2] Bourbaki, Chapters 4-6, Elements of Mathematics (2002) · Zbl 0983.17001 [3] Deligne, Lecture Notes in Math pp 123– (1971) [4] Deligne, Automorphic Forms, Representations and L-functions pp 247– (1977) [5] Deligne, Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math pp 9– (1982) [6] Demazure, Vols. II-III, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), Lecture Notes in Math (1970) [7] Harder, Über die Galoiskohomologie halbeinfacher Matrizengruppen II, Math. Z. 92 pp 396– (1966) · Zbl 0152.01001 [8] Helgason, Pure and Applied Mathematics Vol. 80 (1978) [9] Kottwitz, Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (2) pp 373– (1992) · Zbl 0796.14014 [10] Milne, The Zeta Functions of Picard Modular Surfaces pp 153– (1992) [11] Milne, Motives pp 447– (1991) [12] Mumford, Third edition, Ergebnisse der Math. und ihrer Grenzgebiete (1994) [13] Serre, Journées de Géom. Alg. de Rennes pp 155– (1978) [14] Shimura, On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math. (2) 78 (1) pp 149– (1963) · Zbl 0142.05402 [15] Tate, Proceedings of a Conference on Local Fields (Driebergen, 1966) pp 158– (1967) [16] Tits, Automorphic Forms, Representations and L-functions pp 29– (1977) [17] Vasiu, Integral canonical models of Shimura varieties of preabelian type, Asian J. Math. 3 (2) pp 401– (1999) · Zbl 1002.11052 [18] Vasiu, A purity theorem for abelian schemes, Michigan Math. J. 52 (1) (2004) · Zbl 1069.14049 [19] Vasiu, Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part I, J. Ramanujan Math. Soc. 27 (4) pp 425– (2012) · Zbl 1357.11062 [20] Vasiu, Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic, Doc. Math. 15 pp 571– (2010) · Zbl 1252.11050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.