Further counterexamples to the integral Hodge conjecture

2016/01/22 by Arnav Tripathy, Tripathy, Arnav
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.1601.06170

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arxiv created 2016/01/22 · arxiv updated 2016/01/26

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 ℓ-adic Tate conjecture from the cases ℓ = 2, 3 to all primes ℓ.

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