ELEMENTARY MODULAR IWASAWA THEORY - Hida Haruzo

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Résumé :
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:Iwasawa's proof...

Biographie:
a level-headed description of the p-adic interpolation of modular forms and p-adic L-functions, which are developed into a modular deformation theory...

Sommaire:
a modular version of Iwasawa's discovery by Kubert-Lang as an introduction to modular forms...