Morel Homotopy Modules and Milnor-Witt Cycle Modules

Niels Feld

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arXiv · 1912.12680

Morel Homotopy Modules and Milnor-Witt Cycle Modules

Niels Feld

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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.

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BibTeX RIS

Niels Feld. 2019-12-29. Morel Homotopy Modules and Milnor-Witt Cycle Modules. https://arxiv.org/abs/1912.12680

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