Finite dimensional motives and the Conjectures of Beilinson and Murre

  title={Finite dimensional motives and the Conjectures of Beilinson and Murre},
  author={Vladimir Guletskǐı and Claudio Pedrini},
Let k be a field of characteristic 0 and let Vk be the category of smooth projective varieties over k. By ∼ we denote an adequate equivalence relation for algebraic cycles on varieties [Ja00]. For every X ∈ Vk let A i ∼(X) = (Z (X)/ ∼)⊗Q be the Chow group of codimension i cycles on X modulo the chosen relation ∼ with coefficients in Q. Let X, Y ∈ Vk, let X = ∪Xi be the connected components of X and let di = dim(Xi). Then Corr r ∼(X, Y ) = ⊕iA di+r ∼ (Xi × Y ) is called a space of… CONTINUE READING
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