Beilinson-Tate cycles on semiabelian varieties

Details Beilinson-Tate cycles on semiabelian varieties Beilinson-Tate cycles on semiabelian varieties

2009-09-14

arxiv.org/abs/0909.2670v2

Mathematics

Algebraic Geometry

This is an improved version. "Strong" form of Beilinson's Hodge and Tate conjectures for the varieties under consideration hav

Scientific paper

Along the lines of Hodge and Tate conjectures, Beilinson conjectured that in the qth cohomology all the weight 2q Hodge cycles of a smooth complex variety and all the weight 2q Tate cycles of a smooth variety over a finitely generated field comes from the higher Chow groups. For product of curves and semiabelian varieties, Beilinson-Hodge conjecture was shown in a previous paper by the authors. Here both Beilinson-Hodge and Beilinson-Tate conjectures are shown to be true for varieties dominated by product of curves. We also show that lower weight Hodge cycles (resp. Tate cycles) are algebraic in these situations.

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