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$\mathbb A^{1}$–connected
components of ruled surfaces
Chetan Balwe and Anand Sawant |
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Geometry & Topology 26 (2022) 321–376
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DOI: 10.2140/gt.2022.26.321
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Abstract |
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A conjecture of Morel asserts that the sheaf of –connected components of a space is –invariant. Using purely algebrogeometric methods, we determine the sheaf of –connected components of a smooth projective surface, which is birationally ruled over a curve of genus . As a consequence, we show that Morel’s conjecture holds for all smooth projective surfaces over an algebraically closed field of characteristic . |
Keywords
$\mathbb A^1$–connected components, ghost homotopies, ruled
surfaces
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Mathematical Subject Classification
Primary: 14F42, 55Q05
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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
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Authors |
| Chetan Balwe | |
| Department of Mathematical
Sciences Indian Institute of Science Education and Research Mohali India |
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| Anand Sawant | |
| School of Mathematics Tata Institute of Fundamental Research Mumbai India |
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