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On the unramified cohomology of certain quotient varieties

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Abstract

In this note, we consider unramified cohomology with \({{\mathbb {Z}}}/2\) coefficients for some (degree two) quotient varieties and describe a method that allows one to prove the non-vanishing of these groups under certain conditions. We apply this method to prove a non-vanishing statement in the case of Kummer varieties. Combining this with work of Colliot-Thélène and Voisin, we obtain a new type of three-dimensional counterexample to the integral Hodge conjecture.

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Acknowledgements

The author would like to thank Olivier Benoist for his feedback and for finding a mistake in a previous draft (that led to this draft). He would also like to thank John Christian Ottem for his interest. Finally, many thanks to the excellent referee for carefully reading this paper and providing many useful comments.

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  1. Department of Mathematics, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Humberto Diaz

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  1. Humberto Diaz
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Diaz, H. On the unramified cohomology of certain quotient varieties. Math. Z. 296, 261–273 (2020). https://doi.org/10.1007/s00209-019-02432-4

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