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Hilbert Modular Forms and Iwasawa Theory$
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Haruzo Hida

Print publication date: 2006

Print ISBN-13: 9780198571025

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571025.001.0001

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Hilbert Modular Forms and Iwasawa Theory

Haruzo Hida

Oxford University Press

This introductory chapter describes the deformation theoretic techniques of Wiles-Taylor for elliptic modular forms. The chapter concentrates mostly on the Galois side of the picture, recalling the basic definitions of Iwasawa modules, deformation theory, Iwasawa-theoretic Selmer groups of a nearly p-ordinary Galois representation, and L-invariants. Although Hilbert modular forms are not defined in this chapter, (p-adic families of) elliptic modular forms and their Galois representations are introduced. The main statements about the themes, which are developed later in the book, are stated in this elliptic modular setting, and sketches of the proof are given.

Keywords:   Iwasawa theory, Ordinary Galois representation, Selmer groups, Lambda-adic forms, L-invariant, Galois deformation ring

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