Splitting of abelian varieties in motivic stable homotopy category

Fuente: arXiv
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Main Author: Liu, Haoyang
Format: Preprint
Published: 2024
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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