On the unramified cohomology of certain quotient varieties

2019/06/15 by Diaz, Humberto A.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.06598

Abstract

In this note, we consider unramified cohomology with 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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