The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
نویسنده
چکیده
Recall first that a weight k Hodge structure (L,L) has coniveau c ≤ k2 if the Hodge decomposition of LC takes the form LC = Lk−c,c ⊕ Lk−c−1,c+1 ⊕ . . .⊕ Lc,k−c with Lk−c,c 6= 0. If X is a smooth complex projective variety and Y ⊂ X is a closed algebraic subset of codimension c, then Ker (H(X,Q) → H(X \ Y,Q)) is a sub-Hodge structure of coniveau ≥ c of H(X,Q) (cf. [32, Theorem 7]). The generalized Hodge conjecture formulated by Grothendieck [10] is the following.
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