{"id":"openai-math/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields","pdf":"https://github.com/openai/math/blob/main/preprints/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026","tags":["number-theory","modularity","elliptic-curves"],"score":0,"title":"Modularity of elliptic curves over imaginary quadratic fields","domain":"Number theory","family":"030","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove the modularity conjecture for elliptic curves over imaginary quadratic fields: every such curve is modular, with matching local parameters at every place.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-10-04","reactions":{},"discussion":[{"url":"https://galoisrepresentations.org/2026/10/08/a-brief-digest-of-some-new-openai-results/#:~:text=It%E2%80%99s%20a%20really%20nice%20trick%20rather%20than%20a%20fundamental%20breakthrough.","kind":"web","site":"galoisrepresentations.org","text":"It’s a really nice trick rather than a fundamental breakthrough. I’m sure variations of it will be useful in other ways, and this is definitely worth exploring. Fontaine–Mazur modularity at the prime \\(2\\). It’s a little bit hard for me to see exactly what the new idea is in this 70-plus-page…","added":"2026-10-24","title":"A Brief Digest of Some New OpenAI Results | Persiflage","author":"Persiflage"}],"formalized":false,"family_title":"Modularity of elliptic curves over imaginary quadratic fields"}