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Hilbert Modular Forms and Iwasawa Theory
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Hilbert Modular Forms and Iwasawa Theory

Haruzo Hida

Abstract

The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and applications of the theorem that have been found. Applications include a proof of the torsion of the adjoint Selmer group (over a totally real field F and over the Iwasawa tower of F) and an explicit formula of the L-invariant of the arithmetic p-adic adjoint L-functions. ... More

Keywords: Wiles, Taylor-Wiles, R=T theorem, adjoint Selmer group, anticyclotomic Iwasawa module, Mazur-Tate-Teitelbaum, Greenberg-Stevens, CM fields

Bibliographic Information

Print publication date: 2006 Print ISBN-13: 9780198571025
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780198571025.001.0001

Authors

Affiliations are at time of print publication.

Haruzo Hida, author
University of California, Los Angeles

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