Vol. 6, No. 3, 2012

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
$\mathscr{L}$-invariants and Shimura curves

Samit Dasgupta and Matthew Greenberg

Vol. 6 (2012), No. 3, 455–485
Abstract

In earlier work, the second named author described how to extract Darmon-style -invariants from modular forms on Shimura curves that are special at p. In this paper, we show that these -invariants are preserved by the Jacquet–Langlands correspondence. As a consequence, we prove the second named author’s period conjecture in the case where the base field is . As a further application of our methods, we use integrals of Hida families to describe Stark–Heegner points in terms of a certain Abel–Jacobi map.

Keywords
L-invariants, Shimura curves, Hida families, Stark–Heegner points
Mathematical Subject Classification 2000
Primary: 11F41
Secondary: 11G18, 11F67, 11F75
Milestones
Received: 15 July 2010
Revised: 8 April 2011
Accepted: 23 May 2011
Published: 5 July 2012
Authors
Samit Dasgupta
Department of Mathematics
University of California, Santa Cruz
1156 High St
Santa Cruz, CA 95064
United States
http://people.ucsc.edu/~sdasgup2/
Matthew Greenberg
Department of Mathematics and Statistics
University of Calgary
Calgary, AL T2N 1N4
Canada