AIProofWatch
← Explore interestsIndividual problem

Modularity over imaginary quadratic fields

Modularity over the rationals and known special classes over other fields do not supply the unrestricted imaginary-quadratic result.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

Modularity over the rationals and known special classes over other fields do not supply the unrestricted imaginary-quadratic result. Matching good-prime point counts alone is also a narrower assertion.

The base fields are imaginary quadratic. The statement does not claim modularity for elliptic curves over all number fields or all higher-dimensional abelian varieties.

Why it matters

If correct, establishes the unrestricted imaginary-quadratic elliptic-curve modularity target with full local compatibility.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The base fields are imaginary quadratic. The statement does not claim modularity for elliptic curves over all number fields or all higher-dimensional abelian varieties.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.