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.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.