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arXiv · 1911.05549

A^1-connected components of ruled surfaces

Chetan Balwe·Anand Sawant
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Abstract

A conjecture of Morel asserts that the sheaf of $\mathbb A^1$-connected components of a space is $\mathbb A^1$-invariant. Using purely algebro-geometric methods, we determine the sheaf of $\mathbb A^1$-connected components of a smooth projective surface, which is birationally ruled over a curve of genus $>0$. As a consequence, we show that Morel's conjecture holds for all smooth projective surfaces over an algebraically closed field of characteristic $0$.

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Chetan Balwe, Anand Sawant. 2019-11-13. A^1-connected components of ruled surfaces. https://doi.org/10.2140/gt.2022.26.321

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