A^1-connected components of ruled surfaces

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 $0$.

41 pages, final version before page proofs, accepted for publication in Geometry and Topology

Cited by in corpus (1)

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