On the Chow ring of certain rational cohomology tori

Published 4 Mar 2016 in math.AG | (1603.01426v1)

Abstract: Let $f: X \rightarrow A$ be an abelian cover from a complex algebraic variety with quotient singularities to an abelian variety. We show that $f^*$ induces an isomorphism between the rational cohomology rings $H^\bullet(A, \mathbb{Q})$ and $H^\bullet(X, \mathbb{Q})$ if and only if $f^*$ induces an isomorphism between the Chow rings with rational coefficients $\mathrm{CH}^{\bullet(A)_{\mathbb{Q}}$} and $\mathrm{CH}^{\bullet(X)_{\mathbb{Q}}$.}