Volume 26, issue 1 (2022)

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$\mathbb A^{1}$–connected components of ruled surfaces

Chetan Balwe and Anand Sawant

Geometry & Topology 26 (2022) 321–376
DOI: 10.2140/gt.2022.26.321
Abstract

A conjecture of Morel asserts that the sheaf of 𝔸1–connected components of a space is 𝔸1–invariant. Using purely algebrogeometric methods, we determine the sheaf of 𝔸1–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.

Keywords
$\mathbb A^1$–connected components, ghost homotopies, ruled surfaces
Mathematical Subject Classification
Primary: 14F42, 55Q05
References
Publication
Received: 20 July 2020
Revised: 14 January 2021
Accepted: 17 February 2021
Published: 5 April 2022
Proposed: Mark Gross
Seconded: Haynes R Miller, Mark Behrens
Authors
Chetan Balwe
Department of Mathematical Sciences
Indian Institute of Science Education and Research
Mohali
India
Anand Sawant
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India