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On anticyclotomic μ-invariants of modular forms

Part of: Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  27 July 2011

Robert Pollack  and
Tom Weston
Robert Pollack
Affiliation:
Department of Mathematics, Boston University, Boston, MA, USA (email: rpollack@math.bu.edu)
Tom Weston
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, MA, USA (email: weston@math.umass.edu)
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Abstract

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We prove the μ-part of the main conjecture for modular forms along the anticyclotomic Zp-extension of a quadratic imaginary field. Our proof consists of first giving an explicit formula for the algebraic μ-invariant, and then using results of Ribet and Takahashi showing that our formula agrees with Vatsal’s formula for the analytic μ-invariant.

Keywords

Iwasawa theorymodular formsanticyclotomicμ invariantsmain conjecture

MSC classification

Secondary: 11R23: Iwasawa theory 11F33: Congruences for modular and $p$-adic modular forms
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 5 , September 2011 , pp. 1353 - 1381
Copyright
Copyright © Foundation Compositio Mathematica 2011

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