Abstract
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.
Original language | English (US) |
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Pages (from-to) | 923-1000 |
Number of pages | 78 |
Journal | Algebra and Number Theory |
Volume | 5 |
Issue number | 6 |
DOIs | |
State | Published - 2011 |
Keywords
- Arithmetic inner product formula
- Arithmetic theta lifting
- L-derivatives
- Unitary Shimura curves
ASJC Scopus subject areas
- Algebra and Number Theory