Serre-Tate Theory for Moduli Spaces of PEL Type

Details Serre-Tate Theory for Moduli Spaces of PEL Type Serre-Tate Theory for Moduli Spaces of PEL Type

2002-03-28

arxiv.org/abs/math/0203288v2

Mathematics

Algebraic Geometry

Plain TeX, 44 pages. This is a completely revised version of our March 2002 preprint; part of the results are now given in a s

Scientific paper

The main goal of this paper is to generalize Serre-Tate theory of "ordinary" local moduli to Shimura varieties of PEL type. To this end we develop a generalized notion of ordinariness, we prove a number of basic results about this, and we study the formal deformations of ordinary objects. In general, the formal deformation spaces get a new "group-like" structure that we call a "cascade". Further the paper contains some results on the Ekedahl-Oort stratification of PEL moduli spaces, and an application of our results to the study of congruence relations.

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