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Beilinson-Hodge cycles on semiabelian varieties

Algebraic Geometry 2009-02-24 v2 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.0808.2990,
  title  = {Beilinson-Hodge cycles on semiabelian varieties},
  author = {Donu Arapura and Manish Kumar},
  journal= {arXiv preprint arXiv:0808.2990},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:12:49.067Z