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Cycle modules and mixed motives. (Modules de cycles et motifs mixtes.) (French. Abridged English version) Zbl 1042.19001
Summary: For a perfect field \(k\), we give a relation between the category of homotopy invariant sheaves with transfers defined by Voevodsky and the category of cycle modules defined by Rost. More precisely, the category of cycle modules over \(k\) is equivalent to the category obtained from the homotopy invariant sheaves with transfers by formally inverting the sheaf represented by \(\mathbb{G}_m\) with its canonical structure of a presheaf with transfers. This gives a canonical monoidal structure on the category of cycle modules over \(k\), and shows that it is abelian.

MSC:
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
14C25 Algebraic cycles
19D45 Higher symbols, Milnor \(K\)-theory
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