INTRODUCTION

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...

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Published in: Hilbert Modular Forms and Iwasawa Theory
Main Author: Hida, Haruzo
Format: Book Chapter
Language: English
Published: Oxford Oxford University Press 06-15-2006
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Summary: 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.
ISBN: 9780198571025
019857102X
DOI: 10.1093/acprof:oso/9780198571025.003.0001