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arXiv · 2009.14800

The freeness property for locally nilpotent derivations of k[x,y,z]

Daniel Daigle
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Abstract

We prove Freudenburg's Freeness Conjecture: Let B be the polynomial ring in three variables over a field of characteristic zero, let D : B --> B be a nonzero locally nilpotent derivation, and let A = ker(D). Then B is a free A-module, and there exists a basis $(e_i)_{i \in \mathbb{N}}$ of B such that deg$_D(e_i) = i$ for all $i \in \mathbb{N}$.

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Daniel Daigle. 2020-09-30. The freeness property for locally nilpotent derivations of k[x,y,z]. https://arxiv.org/abs/2009.14800

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