Stable coordinate conjecture

Let AA be a commutative ring with one, let A[n]A^{[n]} denote a polynomial ring in nn variables over AA, and let fA[n]f\in A^{[n]}. A polynomial ff is a stable coordinate if it is a coordinate in A[n+m]A^{[n+m]} for some mNm\in\mathbb{N}. Stable coordinate conjecture. If AA is a Q\mathbb{Q}-algebra and ff is a stable coordinate, then ff is a coordinate of A[n]A^{[n]}. The conjecture asks whether stabilization can create coordinates that were not already coordinates. Its status is not resolved in the supplied text.

Sources & referencesView supporting material

Primary source

Drew Lewis, “Venereau-type polynomials as potential counterexamples”, arXiv:1007.2230 (2012).

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