Motivic spectra and universality of K-theory

2022/04/07 by Toni Annala, Annala, Toni, Ryomei Iwasa +1 · 4 citations
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.2204.03434

openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a theory of motivic spectra in a broad generality; in particular \mathbbA¹-homotopy invariance is not assumed. As an application, we prove that K-theory of schemes is a universal Zariski sheaf of spectra which is equipped with an action of the Picard stack and satisfies projective bundle formula.

Cited by

• Nilpotence of η in étale motivic spectra
• How to invert well-pointed endofunctors
• Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology
• Beilinson--Lichtenbaum phenomenon for motivic cohomology

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