Volume 26, issue 1 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
$\mathbb A^{1}$–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