E-motives and motivic stable homotopy

2017/04/25 by Le Dang Thi Nguyen, Nguyen, Le Dang Thi
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1704.07672

openalex publication_date 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce in this work the notion of the category of pure E-Motives, where E is a motivic strict ring spectrum and construct twisted E-cohomology by using six functors formalism of J. Ayoub. In particular, we construct the category of pure Chow-Witt motives CHW(k)_ℚ over a field k and show that this category admits a fully faithful embedding into the geometric stable \mathbbA¹-derived category D_\mathbbA¹,gm(k)_ℚ.

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