On the Chow ring of certain rational cohomology tori
Zhi Jiang, Qizheng Yin

TL;DR
This paper investigates conditions under which an abelian cover between complex algebraic varieties induces isomorphisms in rational cohomology and Chow rings, revealing a deep connection between these algebraic invariants.
Contribution
It establishes an equivalence between isomorphisms in rational cohomology rings and Chow rings for abelian covers of varieties with quotient singularities.
Findings
Isomorphism in cohomology implies isomorphism in Chow rings.
Characterization of when pullback induces ring isomorphisms.
Connection between topological and algebraic cycle invariants.
Abstract
Let be an abelian cover from a complex algebraic variety with quotient singularities to an abelian variety. We show that induces an isomorphism between the rational cohomology rings and if and only if induces an isomorphism between the Chow rings with rational coefficients and .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics
