This is an update on the talk I gave about 10 years ago on this seminar. The arithmetic Gan-Gross-Prasad (AGGP) conjecture, a high dimensional generalization of the Gross–Zagier theorem, relates the height pairing of arithmetic diagonal cycles on certain product Shimura varieties to the first central derivative of Rankin-Selberg tensor product L-functions. The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to the AGGP conjecture. I will recall the statement of the arithmetic fundamental lemma and present (a sketch of) a proof.
Joint IAS/Princeton University Number Theory Seminar
The arithmetic fundamental lemma for unitary groups: an update
Massachusetts Institute of Technology
Date & Time
December 12, 2019 | 4:30 – 5:30pm
Princeton University, Fine 214