Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 030. Modularity over imaginary quadratic fields
Family claims › Number theory · lines 367–372
OpenAI@2026-10-07#rem:oai-030
Proves the modularity conjecture for elliptic curves over imaginary quadratic fields: every elliptic curve over every imaginary quadratic field is modular, with matching local parameters at every place.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 001. Milne's rationality conjecture
- remark: Remark: Family 002. The full Birch–Swinnerton-Dyer formula in Selmer coranks zero and one
- remark: Remark: Family 003. The quasi-Riemann hypothesis
- remark: Remark: Family 004. Hilbert's tenth problem over Q
- remark: Remark: Family 005. Irrationality of Catalan's constant
- remark: Remark: Family 006. Goldfeld's conjecture
- remark: Remark: Family 007. Two-point Chowla and the corrected binary Elliott conjecture
- remark: Remark: Family 008. The Deligne–Drinfeld conjecture