6533b873fe1ef96bd12d5724

RESEARCH PRODUCT

Milnor-Witt Motives

Tom BachmannBaptiste CalmèsFrédéric DégliseJean FaselPaul Arne ØStvær

subject

Mathematics - Algebraic GeometryMathematics::K-Theory and HomologyMathematics::Category Theory11E70 13D15 14F42 19E15 19G38 (Primary) 11E81 14A99 14C35 19D45 (Secondary)FOS: Mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)Mathematics::Algebraic Topology

description

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.

yearjournalcountryeditionlanguage
2020-09-18
https://hal.science/hal-03014211