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Further counterexamples to the integral Hodge conjecture · Around

2016

Further counterexamples to the integral Hodge conjecture

Tripathy, Arnav

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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 $\ell$.

Built on

Analytic cycles on complex manifolds
M. F. Atiyah and F. Hirzebruch · 1962
Earlier work this paper cites.
Projective dimension and Brown-Peterson homology
David Copeland Johnson and W. Stephen Wilson · 1973
Earlier work this paper cites.
The Ω \Omega -spectrum for Brown-Peterson cohomology. II
W. Stephen Wilson · 1975
Earlier work this paper cites.
Trento examples
János Kollár · 1992
Earlier work this paper cites.
Torsion algebraic cycles and complex cobordism
Burt Totaro · 1997
Earlier work this paper cites.

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Then

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