English

Morel Homotopy Modules and Milnor-Witt Cycle Modules

Algebraic Geometry 2021-02-18 v2

Abstract

We study the cohomology theory and the canonical Milnor-Witt cycle module associated to a motivic spectrum. We prove that the heart of Morel-Voevodsky stable homotopy category over a perfect field (equipped with its homotopy t-structure) is equivalent to the category of Milnor-Witt cycle modules, thus generalising D\'eglise's thesis. As a corollary, we recover a theorem of Ananyevskiy and Neshitov and we prove that the Milnor-Witt K-theory groups are birational invariants.

Keywords

Cite

@article{arxiv.1912.12680,
  title  = {Morel Homotopy Modules and Milnor-Witt Cycle Modules},
  author = {Niels Feld},
  journal= {arXiv preprint arXiv:1912.12680},
  year   = {2021}
}
R2 v1 2026-06-23T12:58:28.175Z