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2022 A1–connected components of ruled surfaces
Chetan Balwe, Anand Sawant
Geom. Topol. 26(1): 321-376 (2022). 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.

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Chetan Balwe. Anand Sawant. "A1–connected components of ruled surfaces." Geom. Topol. 26 (1) 321 - 376, 2022. https://doi.org/10.2140/gt.2022.26.321

Information

Received: 20 July 2020; Revised: 14 January 2021; Accepted: 17 February 2021; Published: 2022
First available in Project Euclid: 9 May 2022

Digital Object Identifier: 10.2140/gt.2022.26.321

Subjects:
Primary: 14F42 , 55Q05

Keywords: A1–connected components , ghost homotopies , ruled surfaces

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.26 • No. 1 • 2022
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