AFL over F
I will report on the recent proof of the AFL over a general p-adic local field (p > n). The previous proof of the AFL (due to W. Zhang) was restricted to Q_p since it relied on the modularity of Kudla divisor generating series on integral models of unitary Shimura varieties, which is only known over Q. The new proof merely requires modularity for the generic fiber generating series, allowing us to work with an arbitrary totally real field. This is joint work with W. Zhang.