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Number theory

Modularity of elliptic curves over imaginary quadratic fields

OpenAI research collection · 1 manuscript · Source checked 2026-10-19

OpenAI's result summary

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.

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MANUSCRIPT 01

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.

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