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arXiv · 2104.12575

Plectic Stark-Heegner points

Michele Fornea·Lennart Gehrmann
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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.

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Michele Fornea, Lennart Gehrmann. 2021-04-26. Plectic Stark-Heegner points. https://arxiv.org/abs/2104.12575

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