2025/09/22 by Scavia, Federico, Suzuki, Fumiaki
#510 #Algebraic cycles #Integral Tate conjecture #Unramified cohomology
paper · doi:10.15488/19688
We give the first examples of smooth projective varieties X over a finite field F admitting a non-algebraic torsion ℓ-adic cohomology class of degree 4 which vanishes over F‾. We use them to show that two versions of the integral Tate conjecture over F are not equivalent to one another and that a fundamental exact sequence of Colliot-Thélène and Kahn does not necessarily split. Some of our examples have dimension 4, and are the first known examples of fourfolds with non-vanishing Hnr3(X,Q2/Z2(2)).