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 Nekovar-Scholl's notion of plectic Hodge structures. Moreover, we construct exotic Abel-Jacobi maps sending certain zero cycles on QSVs to plectic Jacobians.
PLECTIC JACOBIANS
Fornea M.
2024
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 Nekovar-Scholl's notion of plectic Hodge structures. Moreover, we construct exotic Abel-Jacobi maps sending certain zero cycles on QSVs to plectic Jacobians.
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