Abstract
We prove the arithmetic inner product formula conjectured in the first paper of this series for , that is, for the group unconditionally. The formula relates central -derivatives of weight- holomorphic cuspidal automorphic representations of with -factor 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 of square-free level.
Citation
Yifeng Liu. "Arithmetic theta lifting and $L$-derivatives for unitary groups, II." Algebra Number Theory 5 (7) 923 - 1000, 2011. https://doi.org/10.2140/ant.2011.5.923
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