Plectic Jacobians
Copyright policy )Plectic Jacobians
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.
- University of Padua Italy
- Mathematical Sciences Research Institute United States
\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Mathematics - Number Theory, Abel-Jacobi map, Modular and Shimura varieties, plectic Hodge structure, Heegner point, Mathematics - Algebraic Geometry, FOS: Mathematics, quaternionic Shimura variety, Number Theory (math.NT), Jacobians, Prym varieties, Arithmetic aspects of modular and Shimura varieties, Algebraic Geometry (math.AG), plectic Jacobian
\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Mathematics - Number Theory, Abel-Jacobi map, Modular and Shimura varieties, plectic Hodge structure, Heegner point, Mathematics - Algebraic Geometry, FOS: Mathematics, quaternionic Shimura variety, Number Theory (math.NT), Jacobians, Prym varieties, Arithmetic aspects of modular and Shimura varieties, Algebraic Geometry (math.AG), plectic Jacobian
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!