Notes on Milnor-Witt K-theory
Abstract
These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory with careful attention to twists. A main new contribution is the computation of transfers in the general, in particular inseparable, case using Grothendieck (differential) trace maps. The results provide a complete framework for the functoriality axioms of Milnor-Witt modules and form the basis for an upcoming work on Chow-Witt groups with Niels Feld and Fangzhou Jin.
Keywords
Cite
@article{arxiv.2305.18609,
title = {Notes on Milnor-Witt K-theory},
author = {Frédéric Déglise},
journal= {arXiv preprint arXiv:2305.18609},
year = {2025}
}
Comments
Revised and expanded version, 88 pages. Includes complete proofs of functoriality properties, including (R3b), and a new finer version (R3b+) involving "defects" of DVR. Comments welcome