Liftings of Reduction Maps for Quaternion Algebras

Christophe Cornut, Dimitar Jetchev

Published 2010-12-03Version 1

We construct liftings of reduction maps from 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.