Splitting of abelian varieties in motivic stable homotopy category

2024/06/09 by Haoyang Liu, Liu, Haoyang
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2406.05674

openalex publication_date 2024/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 SH(k). Let k=ℝ, there is a concrete splitting which is determined by the motive of X and the real points X(ℝ) in SH(ℝ)_Λ for some ℤ⊂Λ⊂ℚ. We will also discuss this splitting from a viewpoint of the Chow-Witt correspondences.

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