Plectic Stark-Heegner points
Number Theory
2021-04-27 v1
Abstract
We propose a conjectural construction of global points on modular elliptic curves over arbitrary number fields, generalizing both the p-adic construction of Heegner points via Cerednik-Drinfeld uniformization and the definition of classical Stark-Heegner points. In alignment with Nekovar and Scholl's plectic conjectures, we expect the non-triviality of these plectic Stark-Heegner points to control the Mordell-Weil group of higher rank elliptic curves. We provide some indirect evidence for our conjectures by showing that higher order derivatives of anticyclotomic p-adic L-functions compute plectic invariants.
Cite
@article{arxiv.2104.12575,
title = {Plectic Stark-Heegner points},
author = {Michele Fornea and Lennart Gehrmann},
journal= {arXiv preprint arXiv:2104.12575},
year = {2021}
}