Modularity of elliptic curves over imaginary quadratic fields
We prove the modularity conjecture for elliptic curves over imaginary quadratic fields: every such curve is modular, with matching local parameters at every place.
Cite
@misc{OAI:Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026,
author = {{OpenAI}},
title = {{Modularity of elliptic curves over imaginary quadratic fields}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026/paper.pdf}{OAI:Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026}},
year = {2026}
}