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2012 $\mathscr{L}$-invariants and Shimura curves
Samit Dasgupta, Matthew Greenberg
Algebra Number Theory 6(3): 455-485 (2012). DOI: 10.2140/ant.2012.6.455

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.

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Samit Dasgupta. Matthew Greenberg. "$\mathscr{L}$-invariants and Shimura curves." Algebra Number Theory 6 (3) 455 - 485, 2012. https://doi.org/10.2140/ant.2012.6.455

Information

Received: 15 July 2010; Revised: 8 April 2011; Accepted: 23 May 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1285.11072
MathSciNet: MR2966706
Digital Object Identifier: 10.2140/ant.2012.6.455

Subjects:
Primary: 11F41
Secondary: 11F67 , 11F75 , 11G18

Keywords: Hida families , L-invariants , Shimura curves , Stark–Heegner points

Rights: Copyright © 2012 Mathematical Sciences Publishers

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