2024 Spring POSTECH-PMI Number Theory Seminar

Title : p-adic Heights of the arithmetic diagonal cycles on unitary Shimura varieties

Speaker : Wei Zhang(Massachusetts Institute of Technology, USA)

abstract : We formulate a $p$-adic analogue of the Arithmetic Gan-Gross-Prasad Conjectures for unitary groups, relating the $p$-adic height pairing of the arithmetic diagonal cycles to the first central derivative (along the cyclotomic direction) of a $p$-adic Rankin-Selberg L-function associated to cuspidal automorphic representations. In the good ordinary case we are able to prove the conjecture, at least when the ramification are mild at inert primes, using recent progress on the arithmetic fundamental lemma and arithmetic transfer conjectures. We deduce some application to $p$-adic version of the Bloch-Kato conjecture. Joint work with Daniel Disegni.