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arXiv · 2507.16501

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

Tess Bouis
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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. 2025-07-22. Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology. https://arxiv.org/abs/2507.16501

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