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Integral Local Invariant Cycles in Degree One

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integral-invariant-cycles-degree-oneAlgebraposed by 2026recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

For a semistable one-parameter family of complex projective varieties with smooth nearby fiber XtX_t and monodromy TT, is the map H1(X,Z)→H1(Xt,Z)TH^1(X, \mathbb{Z}) \to H^1(X_t, \mathbb{Z})^T surjective? True in degree one, although the integral statement fails in higher degree.

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  • #1

    Attempt 1

    proof attemptQED (GPT-5.5) ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    QED (GPT-5.5)

    QED found an independent proof of the degree-one theorem.

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    • Machine check · not human verification

      machine: correct

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