Plectic Stark-Heegner points
Michele Fornea, Lennart Gehrmann

TL;DR
The paper introduces a conjectural method to construct global points on modular elliptic curves over any number field, extending existing theories and linking p-adic L-functions to the Mordell-Weil group via plectic Stark-Heegner points.
Contribution
It proposes a new conjectural framework for plectic Stark-Heegner points that generalizes previous constructions and connects p-adic L-functions to elliptic curve ranks.
Findings
Evidence from derivatives of p-adic L-functions supports the conjectures.
The construction extends classical Stark-Heegner points to a broader setting.
The approach aligns with plectic conjectures relating to Mordell-Weil groups.
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Historical Studies and Socio-cultural Analysis
