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Schmidt's measurable rigidity conjecture for mixing zero-entropy algebraic actions
Schmidt's conjecture. If $h(\alpha)=0$ , then $\phi$ is $\lambda_X$ -almost everywhere equal to an affine map. In particular, measurable conjugacy implies algebraic conjugacy.
Conjectureopenalgebraic-dynamics measurable-rigidity zero-entropy-actionsarXiv posted 2 days ago

Schmidt's measurable rigidity conjecture for mixing zero-entropy algebraic actions