Note on the counterexamples for the integral Tate conjecture over finite fields
We discuss some examples of non-torsion and non-algebraic cohomology classes for varieties over finite fields. The approach follows the construction of M. F. Atiyah and F. Hirzebruch [Topology 1, 25--45 (1962; Zbl 0108.36401)] and B. Totaro [J. Am. Math. Soc. 10, No. 2, 467--493 (1997; Zbl 0989.14001)].