Relative \mathbbA¹-homology and its applications

2019/04/18 by Yuri Shimizu, Shimizu, Yuri
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1904.08644

To appear in Homology, Homotopy, and Applications

arxiv created 2021/02/23 · arxiv updated 2021/02/24

Abstract

In this paper, we prove an \mathbbA¹-homology version of the Whitehead theorem with dimension bound. We also prove an excision theorem for \mathbbA¹-homology, Suslin homology and \mathbbA¹-homotopy sheaves. In order to prove these results, we develop a general theory of relative \mathbbA¹-homology and \mathbbA¹-homotopy sheaves. As an application, we compute the relative \mathbbA¹-homology of a hyperplane embedding ℙ^n-1 \hookrightarrow ℙⁿ.

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