We prove the arithmetic inner product formula conjectured in the first paper of this series for n = 1, that is, for the group U(1,1)F unconditionally. The formula relates central L-derivatives of weight-2 holomorphic cuspidal automorphic representations of U(1,1)F with ε-factor -1 with the Néron-Tate height pairing of special cycles on Shimura curves of unitary groups. In particular, we treat all kinds of ramification in a uniform way. This generalizes the arithmetic inner product formula obtained by Kudla, Rapoport, and Yang, which holds for certain cusp eigenforms of PGL(2)Q of square-free level.
- Arithmetic inner product formula
- Arithmetic theta lifting
- Unitary Shimura curves
ASJC Scopus subject areas
- Algebra and Number Theory