Seminar:
Algebra and Number Theory Seminar
Event time:
Tuesday, April 19, 2022 - 4:30pm
Speaker:
Zhiyu Zhang
Speaker affiliation:
MIT
Event description:
For any parahoric Zp2/Zp hermitian lattice, I will formulate and prove an arithmetic transfer identity relating derived intersection numbers on relevant Rapoport–Zink spaces to derivatives of relevant orbital integrals, including the arithmetic fundamental lemma as a special case. As our moduli spaces are usually singular, we resolve the singularity (similar to the Atiyah flop) to define well-behaved intersection numbers.
I will focus on local pictures. These identities have applications towards the arithmetic GGP conjecture for unitary groups, which generalizes the Gross-Zaiger formula on Shimura curves to higher dimensions.
Research area(s):
Algebraic Geometry
Number Theory
Representation Theory