Abstract
In this paper we show that pseudo-canonical liftings do not exist, by showing that if j0 ↦ (j0, J1(j0), J2(j0),…) is the map that gives canonical liftings for ordinary j0, then J2 has a pole at j0 = 1728 if p ≡ 3 ( mod 4) and J3 has a pole at j0 = 0 if p ≡ 5 ( mod 6). Moreover, precise descriptions of J2 and J3 are given.
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