Milnor-Witt Motives
Abstract
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our definition of Milnor-Witt finite correspondences, where our cycles come equipped with quadratic forms. This yields a weaker notion of transfers and a derived category of motives that is closer to the stable homotopy theory of schemes. We prove a cancellation theorem when tensoring with the Tate object, we compare the diagonal part of our Milnor-Witt motivic cohomology to Minor-Witt K-theory and we provide spectra representing various versions of motivic cohomology in the -derived category or the stable homotopy category of schemes.
Cite
@article{arxiv.2004.06634,
title = {Milnor-Witt Motives},
author = {Tom Bachmann and Baptiste Calmès and Frédéric Déglise and Jean Fasel and Paul Arne Østvær},
journal= {arXiv preprint arXiv:2004.06634},
year = {2022}
}
Comments
198 pages. This book is composed of updated versions of arXiv:1412.2989, arXiv:1708.06100, arXiv:1710.00594, arXiv:1708.06102, arXiv:1708.06098 and arXiv:1708.06095, together with an introduction, and an index