Plectic Jacobians
Number Theory
2023-05-16 v2 Algebraic Geometry
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.
Cite
@article{arxiv.2305.01130,
title = {Plectic Jacobians},
author = {Michele Fornea},
journal= {arXiv preprint arXiv:2305.01130},
year = {2023}
}
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