For modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of p-adic primes, we define new p-adic invariants. Inspired by Nekovář and Scholl's plectic conjectures, we believe these invariants control the Mordell–Weil group of higher rank elliptic curves and we support our expectations with numerical experiments.
Plectic p-adic invariants
Fornea M.
;
2022
Abstract
For modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of p-adic primes, we define new p-adic invariants. Inspired by Nekovář and Scholl's plectic conjectures, we believe these invariants control the Mordell–Weil group of higher rank elliptic curves and we support our expectations with numerical experiments.
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