TY  - BOOK
AU  - Hida,Haruzo
TI  - Elementary modular Iwasawa theory
T2  - Series on number theory and its applications,
SN  - 9789811241369
AV  - QA247.3 .H53 2021
U1  - 512.74 HID-H 
PY  - 2022///
CY  - New Jersey
PB  - World Scientific
KW  - Iwasawa theory
KW  - Galois theory
KW  - Modules (Algebra)
N1  - 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
N2  - "The only book available that exposes the Iwasawa theoretic aspects of modular forms and Galois deformation theory The results found in the book are at the cutting edge of the present research The first few chapters provide the fundamentals while the latter chapters cater to first or second-year graduate students Contains numerous open research problems for young researchers"--
ER  -