Elementary Modular Iwasawa Theory (Hardcover)

Elementary Modular Iwasawa Theory By Haruzo Hida Cover Image
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This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows: Many open problems are presented to stimulate young researchers pursuing their field of study.

Product Details
ISBN: 9789811241369
ISBN-10: 9811241368
Publisher: World Scientific Publishing Company
Publication Date: October 27th, 2021
Pages: 448
Language: English