Ananth N. Shankar, Rong Zhou
Published 2016-12-19Version 1
We study the formal neighbourhood of a point in $\mu$-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a shifted cascade. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization in terms of its endomorphisms in analogy with the Serre-Tate canonical lift of an ordinary abelian variety.
Every positive integer is the order of an ordinary abelian variety over ${\mathbb F}_2$
Foliated dynamical systems associated to ordinary abelian varieties over finite fields
Real structures on ordinary Abelian varieties
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