In this talk, we will introduce and study mirabolic special cycles on certain Rapoport-Zink spaces for $GL_n$, which do not exist in the "real" world. Motivated by the arithmetic Gan--Gross--Prasad conjectures, we will formulate a twisted arithmetic fundamental lemma. With the help of these new cycles, we can prove this new AFL.

Time:

15:15 -- 16:15, September 20