# 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 $\mathbb{A}^1$-derived category or the stable homotopy category of schemes.
Document type :
Preprints, Working Papers, ...

https://hal-univ-artois.archives-ouvertes.fr/hal-02942568
Contributor : Baptiste Calmès <>
Submitted on : Friday, September 18, 2020 - 9:23:58 AM
Last modification on : Tuesday, November 24, 2020 - 9:16:03 AM

### Identifiers

• HAL Id : hal-02942568, version 1
• ARXIV : 2004.06634

### Citation

Tom Bachmann, Baptiste Calmès, Frédéric Déglise, Jean Fasel, Paul Arne Østvær. Milnor-Witt Motives. 2020. ⟨hal-02942568⟩

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