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Remarks on iterations of
the $\mathbb A^1$-chain connected components construction
Chetan Balwe, Bandna Rani and Anand Sawant |
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Vol. 7 (2022), No. 2, 385–394
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Abstract |
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We show that the sheaf of -connected components of a Nisnevich sheaf of sets and its universal -invariant quotient (obtained by iterating the -chain connected components construction and taking the direct limit) agree on field-valued points. This establishes an explicit formula for the field-valued points of the sheaf of -connected components of any space. Given any natural number , we construct an -connected space on which the iterations of the naive -connected components construction do not stabilize before the -th stage. |
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Keywords
$\mathbb A^1$-connected components, $\mathbb A^1$-chain
connected components, Morel's conjecture
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Mathematical Subject Classification
Primary: 14F42
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Milestones
Received: 21 July 2021
Revised: 1 February 2022
Accepted: 17 February 2022
Published: 13 September 2022
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Authors |
| Chetan Balwe | |
| Department of Mathematical
Sciences Indian Institute of Science Education and Research Mohali Knowledge City, Sector 81 Mohali India |
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| Bandna Rani | |
| Department of Mathematical
Sciences Indian Institute of Science Education and Research Mohali Knowledge City, Sector 81 Mohali India |
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| Anand Sawant | |
| School of Mathematics Tata Institute of Fundamental Research Mumbai India |
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