On the integral Tate conjecture for finite fields and representation theory

Understand

We describe a new source of counterexamples to the so-called integral Hodge and integral Tate conjectures.

• As in the other known counterexamples to the integral Tate conjecture over finite fields, ours are approximations of the classifying space of some group BG.
• Unlike the other examples, we find groups of type A_n, our proof relies heavily on representation theory, and Milnor's operations vanish on the classes we construct.