On the Beilinson-Hodge conjecture for $H^2$ and rational varieties

Andre Chatzistamatiou

On the Beilinson-Hodge conjecture for $H^2$ and rational varieties

Algebraic Geometry 2011-04-27 v1

Authors: Andre Chatzistamatiou

Abstract

The Beilinson-Hodge conjecture asserts the surjectivity of the cycle map $H^n_M(X,\Q(n)) \to {\rm Hom}_{MHS}(\Q(-n),H^n(X,\Q))$ for all positive integers $n$ and every smooth complex algebraic variety $X$ . For $n=2$ , we prove the conjecture if $X$ is rational.

Keywords

Beilinson-Hodge conjecture cycle map rational varieties motivic cohomology mixed Hodge structures algebraic cycles

Cite

@article{arxiv.1104.4976,
  title  = {On the Beilinson-Hodge conjecture for $H^2$ and rational varieties},
  author = {Andre Chatzistamatiou},
  journal= {arXiv preprint arXiv:1104.4976},
  year   = {2011}
}

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14 pages

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