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Motivic spectra and universality of $K$-theory

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arxiv 2204.03434 v3 pith:DESNFR7G submitted 2022-04-07 math.AG math.ATmath.KT

Toni Annala , Ryomei Iwasa This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords spectratheorymotivicactionapplicationassumedbroadbundle
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abstract

We develop a theory of motivic spectra in a broad generality; in particular $\mathbb{A}^1$-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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology

    math.AG 2025-07 conditional novelty 7.0 of 10

    Mixed characteristic motivic cohomology satisfies Weibel vanishing, the projective bundle formula, comparison to Milnor K-theory, and pro cdh descent.

  2. Schematic Functorialities of Birational Motivic Homotopy Categories

    math.AG 2026-08 conditional novelty 6.0 of 10

    The zeroth birational motivic homotopy category of a unibranch scheme is the product of those of its function fields.

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