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This is a Quantitative Study study.

September 23, 2025Open Access

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

Key Points

Motivic cohomology shows expected properties in mixed characteristic schemes, enhancing understanding of algebraic structures.
Key findings include Weibel's vanishing in algebraic K-theory and the projective bundle formula, broadening applications beyond field-defined schemes.
Comparison to Milnor K-theory underscores the depth of motivic cohomology across differing frameworks, enhancing mathematical integration.
Results extend Elmanto--Morrow's previous findings, suggesting wider implications for research in motivation and cohomological frameworks.

Abstract

We prove that the motivic cohomology of mixed characteristic schemes, introduced in our previous work, satisfies various expected properties of motivic cohomology, including a motivic refinement of Weibel's vanishing in algebraic K-theory, the projective bundle formula, a comparison to Milnor K-theory, and a universal characterisation in terms of pro cdh descent. These results extend those of Elmanto--Morrow to schemes which are not necessarily defined over a field.

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Tess Bouis (Tue,) studied this question.

synapsesocial.com/papers/68d4758931b076d99fa6d35a https://doi.org/https://doi.org/10.48550/arxiv.2507.16501