Plectic Stark–Heegner points

We propose a conjectural construction of determinants of global points on modular elliptic curves over arbitrary number fields, generalizing both the p-adic construction of Heegner points via Čerednik–Drinfeld uniformization and the definition of classical Stark–Heegner points. In alignment with Nekovář 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.