On the arithmetic transfer conjecture for exotic smooth formal moduli spaces

Abstract

In the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary group relative to a ramified quadratic extension of a p-adic field. We prove our conjecture in the case of a unitary group in three variables.

Minor revisions. 91 pages

References in corpus (2)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Multiplicity one Conjectures

Cited by in corpus (13)

• Kudla--Rapoport cycles and derivatives of local densities
• The supersingular locus of unitary Shimura varieties with exotic good reduction
• Arithmetic diagonal cycles on unitary Shimura varieties
• Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
• Weil representation and Arithmetic Fundamental Lemma
• Chow groups and $L$-derivatives of automorphic motives for unitary groups
• On Shimura varieties for unitary groups
• Regular formal moduli spaces and arithmetic transfer conjectures
• Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
• On the supersingular locus of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified prime
• Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
• The Gross-Zagier-Zhang formula over function fields
• An arithmetic intersection conjecture