Algebra & Number Theory
- Algebra Number Theory
- Volume 5, Number 7 (2011), 923-1000.
Arithmetic theta lifting and $L$-derivatives for unitary groups, II
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.
Algebra Number Theory, Volume 5, Number 7 (2011), 923-1000.
Received: 2 April 2010
Revised: 20 October 2010
Accepted: 21 October 2010
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 20G05: Representation theory 11G50: Heights [See also 14G40, 37P30] 11F27: Theta series; Weil representation; theta correspondences
Liu, Yifeng. Arithmetic theta lifting and $L$-derivatives for unitary groups, II. Algebra Number Theory 5 (2011), no. 7, 923--1000. doi:10.2140/ant.2011.5.923. https://projecteuclid.org/euclid.ant/1513729714