Geodesic
Morel homotopy modules and Milnor-Witt cycle modules
Documenta mathematica, Tome 26 (2021), pp. 617-659.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 Déglise'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.
Classification : 14C17, 14C35, 11E81
Keywords: cycle modules, Milnor-Witt \(K\)-theory, Chow-Witt groups, \(\mathbb A^1\)-homotopy, birational invariants 
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     author = {Feld, Niels},
     title = {Morel homotopy modules and {Milnor-Witt} cycle modules},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a40/}
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Feld, Niels. Morel homotopy modules and Milnor-Witt cycle modules. Documenta mathematica, Tome 26 (2021), pp. 617-659. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a40/