Some cases of the Tate conjecture for abelian varieties over finite fields

In 1963, Tate conjectured that the algebraic cycles of a variety can be described in terms of the Galois invariants of certain étale cohomology groups. In this talk, I'll discuss a proof of several new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhin. This is joint work with Santiago Arango-Piñeros and Sam Frengley.