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arXiv · 2004.06634

Milnor-Witt Motives

Tom Bachmann·Baptiste Calmès·Frédéric Déglise·Jean Fasel·Paul Arne Østvær
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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 $\mathbb{A}^1$-derived category or the stable homotopy category of schemes.

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Tom Bachmann, Baptiste Calmès, Frédéric Déglise, Jean Fasel, Paul Arne Østvær. 2022-04-04. Milnor-Witt Motives. https://arxiv.org/abs/2004.06634

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