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

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

2011-04-26

arxiv.org/abs/1104.4976v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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.

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