Further counterexamples to the integral Hodge conjecture

Abstract

We study the integral Hodge conjecture in complex codimension $2$ and $3$ for approximations to the classifying space of groups of type A. In degree two, we prove a conjecture of Ben Antieau, extending his two counterexamples to a general family of groups. In particular, when reduced to a finite field, these spaces extend Antieau's counterexamples to the integral $\ell$-adic Tate conjecture from the cases $\ell =2,3$ to all primes $\ell$.

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References in corpus (1)

• On the Chow rings of classifying spaces for classical groups

Cited by in corpus (1)

• Milnor operations and classifying spaces