Integral invariant cycles in degree-one cohomology
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For a one-parameter complex projective degeneration with simple-normal-crossing central fiber and smooth nearby fiber X_t, the target is surjectivity of H¹(X,Z)→H¹(X_t,Z)^T onto the monodromy invariants.
Why it matters and what counts as progress
Why it matters: It asks for an integral invariant-cycle statement, which a rational-coefficient theorem alone does not supply.
What counts as progress: Prove integral surjectivity onto the monodromy invariants; a rational-coefficient invariant-cycle theorem alone does not establish it.
How the problem developed
QED research team The initial QED report describes an independently generated proof of the integral degree-one invariant-cycle theorem for the stated one-parameter degeneration setting.
QED research team; Yilong Zhang The revised report says Zhang verified and explained QED’s proof. It also notes that a different human proof had already been found independently; the two arguments are distinct.
AI contribution
QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems
For a one-parameter complex projective degeneration with simple-normal-crossing central fiber and smooth nearby fiber X_t, QED proves that H¹(X,Z) maps onto the monodromy-invariant subgroup H¹(X_t,Z)^T.
Sources
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Publication dates and editorial changes.
QED gives an independently checked proof of integral invariant cycles in degree one