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Whether an extension of function fields — e.g. k(x1,...,xn) over k(f1,...,fn) induced by a polynomial or rational map — is separable or inseparable, including Jacobian-determinant criteria for separability and the behavior of such extensions in positive characteristic. Invertibility claims about polynomial maps belong under the Jacobian-conjecture tags; number-field separability claims (CM fields,

A polynomial map in positive characteristic with nonzero Jacobian determinant induces a separable algebraic extension of rational function fields.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Algebraic geometryimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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