Note on the Counterexamples for the Integral Tate Conjecture over Finite Fields

In this note we discuss some examples of non-torsion and non-algebraic cohomology classes for varieties over finite fields. The approach follows the construction of Atiyah-Hirzebruch and Totaro. \medskip \centerline{\it A.S. Merkurjev die natali oblatum.}

2010 Mathematics Subject Classification: Primary 14C15; Secondary 14L30, 55R35

Keywords and Phrases: Chow groups, classifying spaces, cohomology operations, integral Tate conjecture

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