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arXiv · 2406.05674

Splitting of abelian varieties in motivic stable homotopy category

Haoyang Liu
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Abstract

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 $\text{SH}(\mathbb{R})_\Lambda$ for some $\mathbb{Z}\subset\Lambda\subset\mathbb{Q}$. We will also discuss this splitting from a viewpoint of the Chow-Witt correspondences.

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Haoyang Liu. 2024-06-09. Splitting of abelian varieties in motivic stable homotopy category. https://arxiv.org/abs/2406.05674

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