# Angle ranks of abelian varieties

## Location

Zoom

Event Series

Event Type

Seminar

Friday, April 15, 2022 12:00 PM

Kiran Kedlaya (UCSD)

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.