Beilinson-Hodge cycles on semiabelian varieties

Mathematics – Algebraic Geometry

Scientific paper

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6 pages; final revision (to appear Math. Res. Lett.)

Scientific paper

Beilinson conjectured that all rational cycles of type (q,q) on the qth
cohomology of a smooth complex algebraic variety should come from motivic
cohomology. The purpose of this note is to prove this when the variety is a
semiabelian variety or a product of curves. The proof is based on the study of
invariants under the Mumford-Tate group.

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