Mathematical Research Letters

Volume 19 (2012)

Number 1

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

Pages: 149 – 164

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n1.a12

Author

Andre Chatzistamatiou (Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany)

Abstract

The Beilinson–Hodge conjecture asserts the surjectivity of the cycle map\[H^n_M(X,\Q(n)) \to \Hom_{{\rm MHS}}(\Q(-n),H^{n}(X,\Q)),\]for all integers $n\geq 1$ and every smooth complex algebraic variety $X$.For $n=2$, we prove the conjecture if $X$ is rational.

Full Text (PDF format)