Beilinson-Tate cycles on semiabelian varieties - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: Along the lines of Hodge and Tate conjectures, Beilinson conjectured that inthe qth cohomology all the weight 2q Hodge cycles of a smooth complex varietyand all the weight 2q Tate cycles of a smooth variety over a finitely generatedfield comes from the higher Chow groups. For product of curves and semiabelianvarieties, Beilinson-Hodge conjecture was shown in a previous paper by theauthors. Here both Beilinson-Hodge and Beilinson-Tate conjectures are shown tobe true for varieties dominated by product of curves. We also show that lowerweight Hodge cycles resp. Tate cycles are algebraic in these situations.



Author: Donu Arapura, Manish Kumar

Source: https://arxiv.org/







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