Plectic Jacobians

Abstract

ABSTRACT Looking for a geometric framework to study plectic Heegner points, we define a collection of abelian varieties – called plectic Jacobians—using the middle-degree cohomology of quaternionic Shimura varieties (QSVs). The construction is inspired by the definition of Griffiths’ intermediate Jacobians and rests on Nekovář–Scholl’s notion of plectic Hodge structures. Moreover, we construct exotic Abel–Jacobi maps sending certain zero cycles on QSVs to plectic Jacobians.