Beilinson's Hodge Conjecture for K_1 revisited

Details Beilinson's Hodge Conjecture for K_1 revisited Beilinson's Hodge Conjecture for K_1 revisited

2008-01-21

arxiv.org/abs/0801.3236v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

Let U be a smooth quasiprojective complex variety and CH^r(U,1) a special instance of Bloch's higher Chow groups. Jannsen was the first to show that the cycle class map cl_{r,1} from CH^r(U,1) (tensored with Q) to hom_{MHS}(Q(0), H^{2r-1}(U,Q(r)) is not in general surjective, contradicting an earlier conjecture of Beilinson. In this paper, we give a refinement of Jannsen's counterexample, and further show that the aforementioned cycle class map becomes surjective at the generic point.

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