Geodesic
Relative $\mathbb{A}^1$-homology and its applications
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 129-141.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper, we prove an $\mathbb{A}^1$-homology version of the Whitehead theorem with dimension bound. We also prove an excision theorem for $\mathbb{A}^1$-homology, Suslin homology and $\mathbb{A}^1$-homotopy sheaves. In order to prove these results, we develop a general theory of relative $\mathbb{A}^1$-homology and $\mathbb{A}^1$-homotopy sheaves. As an application, we compute the relative $\mathbb{A}^1$-homology of a hyperplane embedding $\mathbb{P}^{n-1} \to \mathbb{P}^n$.
DOI : 10.4310/HHA.2022.v24.n1.a7
Classification : 14F42, 19E15
Keywords: $\mathbb{A}^1$-homology, $\mathbb{A}^1$-homotopy, algebraic geometry 
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Yuri Shimizu. Relative $\mathbb{A}^1$-homology and its applications. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 129-141. doi : 10.4310/HHA.2022.v24.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a7/

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