Modularity of elliptic curves over imaginary quadratic fields
Source: github.com/openai/math/tree/main/preprints/Modularity-of-el…
We prove the modularity conjecture for elliptic curves over imaginary quadratic fields: every such curve is modular, with matching local parameters at every place.
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A Brief Digest of Some New OpenAI Results | Persiflagegaloisrepresentations.orgFrank Calegari
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…