Geodesic
Morel homotopy modules and Milnor-Witt cycle modules
Documenta mathematica, Tome 26 (2021), pp. 617-659 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/dm/824
Classification : 11E81, 14C17, 14C35
Mots-clés : Chow-Witt groups, birational invariants, cycle modules, Milnor-Witt K-theory, A1-homotopy 
@article{10_4171_dm_824,
     author = {Niels Feld},
     title = {Morel homotopy modules and {Milnor-Witt} cycle modules},
     journal = {Documenta mathematica},
     pages = {617--659},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/824},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/824/}
}
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Niels Feld. Morel homotopy modules and Milnor-Witt cycle modules. Documenta mathematica, Tome 26 (2021), pp. 617-659. doi: 10.4171/dm/824

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