Arithmetic theta lifting and L-derivatives for unitary groups, II

Yifeng Liu

doi:10.2140/ant.2011.5.923

Arithmetic theta lifting and L-derivatives for unitary groups, II

Yifeng Liu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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)
Pages (from-to)	923-1000
Number of pages	78
Journal	Algebra and Number Theory
Volume	5
Issue number	6
DOIs	https://doi.org/10.2140/ant.2011.5.923
State	Published - 2011

Keywords

Arithmetic inner product formula
Arithmetic theta lifting
L-derivatives
Unitary Shimura curves

ASJC Scopus subject areas

Algebra and Number Theory

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AB - 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.

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KW - Arithmetic theta lifting

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KW - Unitary Shimura curves

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