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One definition of motivic cohomology for smooth schemes $ X$ over a field, is via Friedlander-Suslin complexes. A refresher (you may skip to the question at the bottom) One defines (1) $ z_n(X,d) :=$ free abelian group generated by all reduced, irreducible closed $ k$ -subschemes $ W\subset X\times(\mathbf{P}^1_k)^d\times\Delta_k^n$ that, with the projection onto $Read more