Murre’s conjectures for certain product varieties
نویسنده
چکیده
Let X be a smooth projective variety over C of dimension d. Let ∆ ⊂ X × X be the diagonal. There is a cohomology class cl(∆) ∈ H(X ×X). In this paper we use Betti cohomology with rational coefficients. There is the Künneth decomposition H(X ×X) ≃ ⊕2d i=0 H (X)⊗H (X). We write cl(∆) = ∑2d i=0 π hom i according to this decomposition. Here π hom i ∈ H (X)⊗ H (X). If the Hodge conjecture is true, then each π i is an algebraic cycle. Murre([Mu],[Mu2]) formulated the following conjecture.
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