New (review) paper: Recent progress on the Tate conjecture

My paper about the Tate conjecture for Bull. AMS is now available to view.

In it I survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely intertwined with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. I conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.

After returning the proofs to the AMS, it occurred to me that it could be helpful to readers if I recommended some available related videos. I was too slow for the AMS’s speedy production, however, so I make the recommendations here.

Videos

F. Charles. K3 surfaces over finite fields: insights from complex geometry (2015).

K. Madapusi Pera. Regular integral models for orthogonal Shimura varieties and the Tate conjecture for K3 surfaces in finite characteristic (2012).

D. Maulik. Finiteness of K3 surfaces and the Tate conjecture (2012).

Photo is from foldedspace.org.