Unramified cohomology and the integral Hodge conjecture

Humberto Diaz
The failure of the integral Hodge conjecture has been known since the famous counterexamples of Atiyah and Hirzebruch. Currently, several methods exist for producing other counterexamples. For instance, a seminal result of Colliot-Thélène and Voisin relates the failure of the integral Hodge conjecture in degree 4 to degree 3 unramified cohomology. After giving a quick overview of this method, I will discuss how it can be used to obtain new counterexamples to the integral Hodge...
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