Angle ranks of abelian varieties

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Kiran Kedlaya’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-04-15-kk (and will be deleted after ~3-7 days).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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