A01=Haruzo Hida
Algebraic Number Theory
Arithmetic Geometry
Artin Representation
Author_Haruzo Hida
Bloch-Kato Conjecture
BlochAcAEURA"Kato Conjecture
Category=PBH
Cyclicity
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Galois Deformation Theory
Galois Representation
Greenberg Conjecture
Hecke Algebra
Hida Family (of Modular Forms)
Iwasawa Theory
Modular Forms
Selmer Group
Product details
- ISBN 9789811241369
- Publication Date: 27 Oct 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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:The continuing chapters provide the level of exposition accessible to graduate students, while the results are the latest. Readers will find:Many open problems are presented to stimulate young researchers pursuing their field of study.
