Torres infinitas sorprendentes. Una introducción a la Teoría de Iwasawa
Torres infinitas sorprendentes. Una introducción a la Teoría de Iwasawa
摘要：
这篇文章是一个基本上自成一体的教科书般的介绍古典和现代岩泽理论的西班牙语。它源于作者在2018年墨西哥数学学会（SMM）年会上发表的一门课程的笔记。它包括代数数论和profinite代数的一些基本知识，Iwasawa代数及其模的理论，关于$\mathbb{Z}_p$ -扩张的类群的结果，Dirichlet特征标的$p$ -adic $L$ -函数及其各种构造（以及$L$ -函数的一些复杂理论），不同公式中的分圆主要猜想及其最重要的含义，和一章关于概括概述对数岩泽理论和概括的主要猜想，以椭圆曲线，动机和ETNC。文本包括参考文献和详细的证明，其中一些是没有在标准文献，是访问任何人与代数的基本知识和一些代数数论。
英文摘要：
This text is a mostly self-contained textbook-like introduction to classical and modern Iwasawa Theory in Spanish language. It grew out of notes for a course that the authors gave at the annual conference of the Mexican Mathematical Society (SMM) in 2018. It covers some preliminaries from algebraic number theory and profinite algebra, the theory of the Iwasawa algebra and its modules, results about class groups in $\mathbb{Z}_p$-extensions, $p$-adic $L$-functions for Dirichlet characters and their various constructions (along with some complex theory of $L$-functions), the cyclotomic main conjecture in different formulations together with its most important implications, and a chapter about generalizations outlining logarithmic Iwasawa theory and generalizations of the Main conjecture to elliptic curves, motives and the ETNC. The text includes references and detailed proofs, some of which are not available in the standard literature, and is accessible for anyone with basic knowledge of algebra and some algebraic number theory.
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