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}
}