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Integral Local Invariant Cycles in Degree One

Algebra · posed by 2026 · solved

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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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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    QED (GPT-5.5)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

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

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    Verified by the contributing domain expert; documented in the QED system paper.

    Repeated from the source; nothing was checked here.

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