Rigid meromorphic cocycles for orthogonal groups

Abstract Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p -adic analogue of Borcherds’ singular theta lift. The values of rigid meromorphic cocycles at special points of an associated p -adic symmetric space are then conjectured to belong to class fields of suitable global reflex fields , suggesting an eventual framework for explicit class field theory beyond the setting of CM fields explored in the treatise of Shimura and Taniyama.