Distinguished liftings and the André-Oort conjecture

Abstract

In this paper we study liftings
of affine varieties from finite fields to number fields, such that the lifted
varieties contain specified “canonical” lifts of points. If this canonical
lifting of points corresponds to the Deuring-Serre-Tate
lift of j-invariants
of ordinary elliptic curves, then the resulting lifting problem is closely
related to the André-Oort conjecture. We explore this
connection, prove some results related to the André-Oort
conjecture, and then apply these results together with other known special
cases of the conjecture to our lifting problems.


Mathematics Subject
Classification (2000): 11G15, 11G35



Quaestiones Mathematicae 25 (2002), 363-380