, Volume 25, Issue 1, pp 1-20
Date: 17 Nov 2008

Irreducibility of the Igusa tower

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We shall give a simple (basically) purely in characteristic p proof of the irreducibility of the Igusa tower over Shimura varieties of PEL type. Our result covers Shimura variety of type A and type C classical groups, in particular, the Siegel modular varieties, the Hilbert-Siegel modular varieties, Picard surfaces and Shimura varieties of inner forms of unitary and symplectic groups over totally real fields.

The author is partially supported by the NSF grants: DMS 0244401, DMS 0456252 and DMS 0753991