Comptes Rendus
Algebraic geometry
Counterexamples to F. Morel’s conjecture on π 0 𝔸 1
Joseph Ayoub1
1 University of Zurich / LAGA - Université Sorbonne Paris Nord
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1087-1090

We exhibit counterexamples to F. Morel’s conjecture on the 𝔸 1 -invariance of the sheaves of connected components of 𝔸 1 -local spaces.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.472

Joseph Ayoub 1

1 University of Zurich / LAGA - Université Sorbonne Paris Nord
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Counterexamples to {F.} {Morel{\textquoteright}s} conjecture on~$\protect \pi _0^{\protect \mathbb{A}^1}$},
     journal = {Comptes Rendus. Math\'ematique},
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Joseph Ayoub. Counterexamples to F. Morel’s conjecture on $\protect \pi _0^{\protect \mathbb{A}^1}$. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1087-1090. doi: 10.5802/crmath.472

[1] Joseph Ayoub Un contre-exemple à la conjecture de 𝔸 1 -connexité de F. Morel, C. R. Math. Acad. Sci. Paris, Volume 342 (2006) no. 12, pp. 943-948 | DOI | MR | Zbl

[2] Olivier Debarre Higher-dimensional algebraic geometry, Universitext, Springer, 2001, xiv+233 pages | DOI | MR | Zbl

[3] Fabien Morel 𝔸 1 -algebraic topology over a field, Lecture Notes in Mathematics, 2052, Springer, 2012, x+259 pages | DOI | MR | Zbl

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