English

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

Algebraic Geometry 2025-07-23 v1 K-Theory and Homology Number Theory

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 KK-theory, the projective bundle formula, a comparison to Milnor KK-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.

Keywords

Cite

@article{arxiv.2507.16501,
  title  = {Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology},
  author = {Tess Bouis},
  journal= {arXiv preprint arXiv:2507.16501},
  year   = {2025}
}

Comments

The contents of arXiv:2412.06635v1 have been divided into two disjoint papers: arXiv:2412.06635v2 and the current paper