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arXiv · 2512.18868

On the generalized Bass--Quillen conjecture in dimension 2

Anastasia Stavrova
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Abstract

Let $A$ be a regular ring of dimension $\le 2$. Let $G$ be a reductive group over $A$ such that its derived group is a split, i.e. a Chevalley--Demazure, semisimple group. We prove that every Zariski-locally trivial principal $G$-bundle over $A[x_1,\ldots,x_n]$ is extended from $A$, for any $n\ge 1$. This result generalizes to split reductive groups the dimension $2$ case of the Bass--Quillen conjecture on finitely generated projective modules, settled in positive by M. P. Murthy.

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Anastasia Stavrova. 2025-12-21. On the generalized Bass--Quillen conjecture in dimension 2. https://arxiv.org/abs/2512.18868

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