Vol. 5, No. 7, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Arithmetic theta lifting and $L$-derivatives for unitary groups, II

Yifeng Liu

Vol. 5 (2011), No. 7, 923–1000
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) of square-free level.

Keywords
arithmetic inner product formula, arithmetic theta lifting, L-derivatives, unitary Shimura curves
Mathematical Subject Classification 2000
Primary: 11G18
Secondary: 20G05, 11G50, 11F27
Milestones
Received: 2 April 2010
Revised: 20 October 2010
Accepted: 21 October 2010
Published: 11 April 2012

Proposed: Richard Taylor
Seconded: Brian Conrad, Hendrik W. Lenstra
Authors
Yifeng Liu
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027
United States