On the Chow ring of certain rational cohomology tori

Abstract

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

6 pages

References in corpus (1)

• Rational cohomology tori