Splitting of abelian varieties in motivic stable homotopy category
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913930780082176 |
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| author | Liu, Haoyang |
| author_facet | Liu, Haoyang |
| contents | In this paper, we discuss the motivic stable homotopy type of abelian varieties. For an abelian variety over a perfect field $k$ with a rational point, it always splits off a top-dimensional cell in motivic stable homotopy category $\text{SH}(k)$. Let $k=\mathbb{R}$, there is a concrete splitting which is determined by the motive of X and the real points $X(\mathbb{R})$ in $\text{SH}(\mathbb{R})_Λ$ for some $\mathbb{Z}\subsetΛ\subset\mathbb{Q}$. We will also discuss this splitting from a viewpoint of the Chow-Witt correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting of abelian varieties in motivic stable homotopy category Liu, Haoyang Algebraic Geometry Algebraic Topology In this paper, we discuss the motivic stable homotopy type of abelian varieties. For an abelian variety over a perfect field $k$ with a rational point, it always splits off a top-dimensional cell in motivic stable homotopy category $\text{SH}(k)$. Let $k=\mathbb{R}$, there is a concrete splitting which is determined by the motive of X and the real points $X(\mathbb{R})$ in $\text{SH}(\mathbb{R})_Λ$ for some $\mathbb{Z}\subsetΛ\subset\mathbb{Q}$. We will also discuss this splitting from a viewpoint of the Chow-Witt correspondences. |
| title | Splitting of abelian varieties in motivic stable homotopy category |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2406.05674 |