algebra / Commutative algebra; differential operators

The Generalized Vanishing Conjecture

Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\Lambda^m(P^m) = 0$ for all large $m$ forces $\Lambda^m(P^m Q) = 0$ for all large $m$. Refuted by an explicit five-variable counterexample.

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algebraAug 7, 2026Significance 15/100Registry: unreviewed

The Generalized Vanishing Conjecture

Prior state unknowndisproved

Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\Lambda^m(P^m) = 0$ for all large $m$ forces $\Lambda^m(P^m Q) = 0$ for all large $m$. Refuted by an explicit five-variable counterexample.

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Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\Lambda^m(P^m) = 0$ for all large $m$ forces $\Lambda^m(P^m Q) = 0$ for all large $m$. Refuted by an explicit five-variable counterexample.

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