Kiran Kedlaya (Apr. 15, 2022):  Angle ranks of abelian varieties
Channel: Algebraic Geometry at Stanford
Date: 2022-04-17

The angle rank of an abelian variety over a finite field (or a CM
abelian variety over C) quantifies the extent to which the Tate
conjecture (or the Hodge conjecture) holds "for trivial reasons"; cases
where this does not happen tend to be rare in practice. Picking up a
thread from some old (1980s and 1990s) results of Tankeev and
Lenstra-Zarhin, we show that in many cases, the Tate conjecture is
forced to hold by the Newton polygon of the abelian variety or the
Galois group of the Frobenius eigenvalues. Joint work with Taylor Dupuy
and David Zureick-Brown.