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We construct liftings of reduction maps from complex multiplication (CM) points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a given conductor and CM points on certain corresponding totally definite quaternion algebras.
Alfio Quarteroni, Francesco Regazzoni
Florent Gérard Krzakala, Lenka Zdeborová